Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.     

准方波脉冲形成网络的理论分析与设计

针对微波驱动源、固态调制器等对宽平顶脉冲源的应用需求,开展了基于脉冲形成网络输出准方波的理论研究与分析设计。首先采用Prony算法获得准方波波形的解析表达式,然后基于最佳一致逼近的优化控制思路,列出极点控制方程,采用数值方法求解非线性方程组,获得优化波形参数。在此基础上采用阻抗函数匹配的算法求解出脉冲形成网络的元件参数初始值,根据工程设计的实际情况舍弃部分参数并对个别参数进行优化后,获得最终的元器件参数。通过理论分析与数值模拟相结合的方法,系统地给出了获取长脉宽、低纹波准方波脉冲形成网络的设计方法以及设计准则。该方法可用于设计任意阶低纹波系数的准方波脉冲源,也可用于设计其他输出波形要求的脉冲源。     

光学元件双转子抛光技术中类高斯型去除函数建模与逼近

在Preston假设基础上,研究并推导了光学元件抛光过程中"花瓣"型截面磨头在双转子运动形式下的去除函数.提出了"花瓣"型截面磨头的离散点弧长表达方法,并讨论了该方法的适用范围;基于离散点弧长法,推导了"花瓣"型截面磨头在双转子运动形式下的去除函数表达式;根据可调步长式曲线逼近原理研究了类高斯型目标去除函数的逼近算法;并得到了类余弦型去除函数的双转子抛光模参量.从而证明了双转子抛光技术可以得到类高斯型去除函数.     

New asymptotic representations of the noncentral t-distribution

New asymptotic approximations of the noncentral t distribution are given a generalization of the Student's t distribution. Using new integral representations, we give new asymptotic expansions not only for large values of the noncentrality parameter but also for large values of the degrees of freedom parameter. In some cases, we accept more than one large parameter. These results are not only in terms of elementary functions, but also in terms of the complementary error function and the incomplete gamma function. A number of numerical tests demonstrate the performance of the asymptotic approximations.     

An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

稳定和不稳定核巨共振性质的相对论研究

在相对论平均场的基态上自洽的相对论无规位相近似(RRPA)理论框架下,研究稳定核和不稳定核的巨共振性质.研究了稳定核²⁰⁸Pb,¹⁴⁴Sm,¹¹⁶Sn,⁹⁰Zr,⁴⁰Ca,¹⁶O和不稳定核Ca同位素链同位旋标量和同位旋矢量集体巨共振激发,并讨论了Dirac海负能核子态和矢量介子空间分量对核的巨共振性质的影响.研究的结果表明,Dirac海负能核子态和矢量介子空间分量对同位旋标量激发有贡献,特别是对重核,而对轻核它的贡献减弱,对于同位旋矢量激发的贡献可忽略.几组常用的相对论平均场非线性模型参量,不仅能成功的描述有限核的基态性质,也能很好地描述核的巨共振激发.对于N/Z极端情况下,同位旋矢量巨偶极激发模式存在低能集体激发,它是由于费密面附近弱束缚核子的激发和同位旋混杂效应 关键词： 相对论无规位相近似 核巨共振     

行星重力的后牛顿近似对卫星作用的估计

将行星重力的广义相对论后牛顿近似应用于木星系统和撞击木星的彗星Shoe maker Levy 9,计算了木星重力的后牛顿改正和它的卫星的进动效应,并与地球月球系统作比较,进行分析和讨论 关键词： 重力的后牛顿近似 木星及其卫星 彗星Shoe maker-Levy 9 广义相对论     

Estimating Magic Numbers Larger Than 126 by Fermi—Yang Liming Method

The Fermi-Yang Liming method is followed and developed to estimate new magic numbers in nuclei with a Woods-Saxon density function.The calculated results predict that the magic number next to 126 should be around 184 and 258.     

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB₂ compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a₀ and c/c₀ on pressure P, the normalized primitive cell volume V/V₀ on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature \Theta_D and the heat capacity C_V on pressure P and temperature T.