拉格朗日投影与常用等角投影间解析变换的复变函数表示

借助复变函数理论讨论了拉格朗日投影与常用等角投影间的解析变换问题,导出了拉格朗日投影正反解的复变函数表达式,在此基础上系统地建立了该投影与高斯投影、墨卡托投影和等角圆锥投影间解析变换的复变函数表示模型。这些复数变换公式是含参考椭球第一偏心率的符号形式,可解决不同参考椭球下的投影变换问题,与传统的实数变换公式相比,其结构更为简单,理论更为严密,便于实际使用。     

The Lagrange and Two-Center Problems in the Lobachevsky Space

The generalization of the two-center problem and the Lagrange problem (a mass point motion under the action of attracting center field and the analog of a constant homogeneous field) to the case of a constant curvature space, in the three-dimensional space of Lobachevsky (³), is investigated in this paper. The integrability of these problems is proved. The bifurcation set in the plane of integrals of motion is constructed and the classification of the domains of possible motion is carried out. An analog of a constant homogeneous field is obtained in the Lobachevsky space.     

亚洲大陆下的地幔流动及其对亚洲地壳的作用力

运用并行Lagrange乘子非协调区域分解法（LMDDM）与并行Lagrange乘子非连续变形分析法（LMDDM）耦合的有限元算法，研究了四维球壳内不可压缩、常粘度牛顿流体非定常地幔流动，在大并行计算机上分别求解了全球15个板块运动的速度场、压力场、温度场和应力场，也包括求解出亚洲大陆下地幔流动的各种物理场，以及对亚洲地壳的作用力．      

An alternative algebraic algorithm to transform Cartesian to geodetic coordinates

The algorithm to transform from 3D Cartesian to geodetic coordinates is obtained by solving the equation of the Lagrange parameter. Numerical experiments show that geodetic height can be recovered to 0.5 mm precision over the range from −6×10⁶ to 10¹⁰ m. Electronic Supplementary Material: Supplementary material is available in the online version of this article at     

The mechanics of spall fracture in rock and concrete

Spalling is a wave-induced dynamic fracture phenomenon. The waves can be either one: elastic, elasto-plastic, or shock waves. From a continuum mechanics point of view, fracture mechanics and wave propagation form the main ingredients in the formation of spalls. Recently, however, micro-structural effects have become important in the initial stages of spall formation in a variety of engineering materials ranging from metals to rock and concrete. From a structural geology point of view, the rock mass cannot be modelled as a continuum. In this case, a discontinuum approach has to be taken where the individual features of the rock mass such as joints and faults need to be taken into account. From an application point of view, spallation is important where rapid loading by explosives, impact, or energy deposition, occurs. The range of applications stretches from blasting in mining engineering to damage prevention to structures under explosive excitation.

This contribution offers a multi-faceted and multi-disciplinary approach to the study of spalling with special attention to analytical and experimental work. The reader is assumed to be somewhat familiar with the basics of continuum mechanics, fracture mechanics, and propagation of elastic, plastic and shock waves. The application to rock and concrete will show the effects of structural geological discontinuities such as open and closed joints - and to some degree also faulting - in rock, as well as the micro-structure of concrete on the (shock) wave field.

Extensive use will be made of time-space diagrams which proved very useful in practical applications to blasting problems [Rossmanith, H.P., 2002, The use of Lagrange diagrams in precise initiation blasting. Part I: two interacting blastholes, Fragblast 6, 104-136].     

Lagrange变分和大气中惯性重力内波的稳定性

本文利用Lagrange变分导出了惯性重力内波的波作用量方程,这种方程与用KWB方法所得到的惯性重力内波的波作用量方程在形式上有所不同,但所得到的结果却与观测事实是一致的。     

Lagrange multiplier-based domain decomposition methods for a non-linear sedimentary basin problem

We present two Lagrange multiplier-based domain decomposition methods for solving iteratively a non-linear sedimentary basin problem. Both methods are Uzawa-type algorithms derived from saddle point equations of Lagrangian and augmented Lagrangian functionals. Numerical experiments show that both methods are scalable with respect to the mesh size.     

Application of the representer method for parameter estimation in numerical reservoir models

A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model. Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method. This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure measurements from a small number of observation wells in between the injection and production wells, but the representer method could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool for applications in reservoir engineering.     

基于HYSPLIT模式的济南机场一次暴雨过程的水汽输送特征分析

利用NCEP再分析资料,结合HYSPLIT轨迹模式对 2018年6月25日发生在济南遥墙国际机场的一次大暴雨过程的水汽条件及输送过程进行分析。结果表明：此次大暴雨的水汽输送通道主要有3支,一支是源自对流层中层的西北气流输送,另一支是西太平洋上副热带高压边缘东南气流输送,第三支是南海上空向北的气流输送,三支通道中,西太平洋通道和南海通道对暴雨的水汽贡献最大,分别为46%和42%,来自西北通道的水汽输送相对较少,它对暴雨的水汽贡献仅为12%;进一步的分析表明,在850 hPa以下的对流层底部,来自西太平洋通道的水汽输送占据主导地位,而在700 hPa以上的对流层中层,则是来自南海通道的水汽输送占据主导地位。     

导航卫星自主定轨中JPL DE星历的简化使用

导航卫星自主定轨中使用原始JPL DE星历不仅数据量较大,而且不容易编码。文中提出了一种简化的星历使用方法,利用对一定间隔的日月位置进行拉格朗日插值,取代原始星历的切比雪夫多项式拟合方法,可以有效减少上行传递的参数个数。通过实验分析得出,在60 d的自主定轨中使用间隔1 d的月球位置和10 d的太阳位置进行插值,可以在保证导航卫星自主定轨精度的基础上,参数个数从404/808个减少为254个。