On a class of variational equations transformable to the Gauss hypergeometric equation

A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.     

关于中尺度对称运动的稳定性及其演变

本文首先建立了中尺度对称运动的Hamihon函数,并用变分原理导出了对称运动稳定的充分条件,然后再用Lagrange变分导出了缓变介质中对称运动的波作用量方程,这种波作用量方程与用WKB方法所得到的结果是相同的。同时,本文进一步讨论了中尺度对称扰动渡包的演变规律,并获得了对称运动发展的判据。     

简单随机模式进一步分析(Ⅰ)——非线性外通函数项处理

本文利用等效线性化法和Fokker-planck方程,对一个简单的非线性随机模式非线性项在不同气候时期的参数化进行了讨论,得到了冰期、间冰期和现代气候的概率分布密度及输出响应特征。     

自引力辐射体系的熵与引力坍缩

本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程，计算了约束在一个球形盒子中的目引力辐射体系的墙（不含中心黑洞和含有中心黑洞两种情况）．与Sorkin等人的计算比较，本文的结果不会出现发散困难，而且体系的总摘（包括中心黑洞的墙）的上阳正好等于坍缩后形成的同质量的黑洞嫡．作者认为，自引力辐射体系坍绩的合理模式是先形成中心黑洞，然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞．在坍缩过程中，任一中间态的媳总是比末态的黑洞墙小，到坍缩过程结束总熵才等于对应的黑洞摘．这一结果为黑洞滴的起源提供了一个合理的解释．     

Synchronization of perturbed non-linear Hamiltonians

We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows.     

Explicit solutions of the three-dimensional inverse problem of dynamics,using the frenet reference frame

Given a two-parameter of three-dimensional orbits, we construct the unit tangent vector, the normal and the binormal which define the Frenet reference frame. In this frame, by writing that the force is conservative, we explicitly obtain the potential as a function of the energy along the trajectories and of its derivatives.Observatoire de Besançon     

纳秒级脉冲信号的波形预测与重构

带宽不够、波形易失真是纳秒级脉冲信号测量中存在的主要问题.以测量系统的方波标定数据为标准建立测量系统的差分方程和卷积两种模型,并分别运用于实际试验的双指数脉冲信号的波形预测和重构中,对比两种模型的信号处理结果发现,卷积模型比差分方程模型更适用于纳秒级脉冲信号的波形预测和重构.     

江苏近10 a高架雷暴特征分析

对2007—2016年发生在江苏地区的冬半年雷暴进行特征分析,筛选出12次典型的高架雷暴天气过程,揭示江苏发生高架雷暴的时空分布特征和典型的环流形势,发现逆温层顶之上的不稳定浅层和上下层强垂直风切变分别为高架雷暴的发生提供弱热力不稳定和强动力不稳定条件。强垂直风切变、850 hPa附近强烈的锋生导致的锋面次级环流,高空槽前正涡度平流随高度增加以及高层辐散、低层辐合造成的抽吸作用,为高架雷暴的发生和维持提供逆温层之上的动力抬升条件。高架雷暴发生时高仰角反射率因子呈现出类似零度层亮带的环形特征,对流单体不断生成在圆环附近。初步归纳了江苏高架雷暴的预报着眼点:500 hPa先后高空槽东移,700 hPa有16 m·s~(-1)以上的西南急流,850 hPa切变线东伸,存在逆温层顶高于1. 5 km,逆温强度大于5℃的较强逆温,0～6 km垂直风切变超过18 m·s~(-1),700 hPa与500 hPa温度差在15℃以上以及700hPa的相对湿度高于80%,且比湿在5～6 g·kg~(-1)。     

Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model, we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics. Four initial perturbation approaches are used in the ensemble forecasting experiments: the random perturbation(RP), the bred vector(BV), the ensemble transform Kalman filter(ETKF), and the nonlinear local Lyapunov vector(NLLV) methods. Results show that,regardless of the method used, the ensemble ave...     

Improvement and Evaluation of the Latest Version of WRF-Lake at a Deep Riverine Reservoir

The WRF-lake vertically one-dimensional(1D) water temperature model, as a submodule of the Weather Research and Forecasting(WRF) system, is being widely used to investigate water–atmosphere interactions. But previous applications revealed that it cannot accurately simulate the water temperature in a deep riverine reservoir during a large flow rate period, and whether it can produce sufficiently accurate heat flux through the water surface of deep riverine reservoirs remains uncertain. In this st...