小波分析在单频GPS快速精密定位中的应用研究

单频GPS快速定位方程是严重病态的,应用最小二乘原理得到的模糊度浮点解大大偏离其准确值,应用LAMBDA方法难以正确地固定模糊度。本文将GPS载波相位双差观测量在不同的小波空间和尺度空间进行分解和重构,去除高频测量噪声,可减小测量噪声对GPS快速定位中病态方程解的影响,提高模糊度浮点解的精度,缩小模糊度搜索空间。实验表明,对于GPS短基线,仅利用1min左右的单频载波观测数据,经过基于haar、db4、coif4和sym4小波的5尺度小波变换后,可获得较准确的模糊度浮点解,应用LAMBDA法可正确地固定模糊度,达到厘米级定位精度。     

Comparison between iterative solution of symmetric and non‐symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner

Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non‐symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi‐minimal residual whereas the latter is solved using the popular bi‐conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non‐symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left–right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non‐symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ‐preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill‐conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd.     

Equilibrium and non-equilibrium of two-arch structures in the solar atmosphere

We have derived a similarity solution in the form of a power series of the nonlinear magnetostatic equilibrium equation and identified the region of convergence in the parameter space. Within this region we have equilibrium configurations, outside it, non-equilibrium configurations. An example of nonlinear equilibrium configuration is shown graphically.

Our results can be used to explain the generation of multi-ribbon flares, the two-arch structures and the structures of the magnetic fields above elongated sunspot groups.     

The maximum mass of neutron stars

Summary. The maximum mass of neutron stars plays an important role in determining the end point of the evolution of massive stars. As the number of stellar mass black holes in binary x-ray sources grows, and as the mass spectrum of the black holes emerges, the value of the maximum mass of neutron stars has acquired great significance. Although it is now more than sixty years since the first attempt by Oppenheimer and Volkoff, no definitive answer can be given. This review will attempt to outline the main difficulties, both conceptual as well as technical, that stand in the way of a reliable estimate of the maximum mass. We shall also highlight how laboratory experiments, as well as astronomical observations, may help to clarify the true nature of the interior of neutron stars. Received 26 November 2001 / Published online 22 April 2002     

基于单位四元数描述的单像空间后方交会

在3维空间里,四元数可以非常方便地表示空间方位、空间向量间的旋转、平移和缩放等关系。将四元数理论引入到摄影测量领域,用单位四元数对坐标旋转矩阵进行描述,提出了一种采用单位四元数描述航摄像片位置与姿态的单张像片空间后方交会新方法。该方法与传统方法相比,在平差时避免了频繁的三角函数运算,不仅收敛速度快,而且精度高。     

A micro-mechanical investigation of the dynamic response and liquefaction of saturated granular soils

A coupled continuum-discrete hydromechanical model was utilized to analyze the meso-scale pore fluid flow and micro-scale solid phase deformation of saturated granular soils. The fluid motion was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid particles. Well established semi-empirical relationships were used to quantify the fluid–particle interactions. Numerical simulations were conducted to investigate the mechanisms of granular deposit liquefaction in the presence of a critical upward pore fluid flow as well as when subjected to a dynamic base excitation. The outcome of these simulations was consistent with experimental observations and revealed valuable information on the micro-mechanical characteristics of soil liquefaction and associated loss of stiffness and strength.     

Refinement of predictive reaeration equations for a typical Indian river

Dissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K₂). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K₂ values computed from these predictive equations have been compared with the K₂ values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.     

Rotating Stratified Heterogeneous Oblate Spheroid in Newtonian Physics

By solving the Euler hydrodynamical equations we have obtained closed form solutions for the angular velocities and pressures of a three stratified non-confocal heterogeneous oblate spheroid. Limiting and particular solutions cases, such as a spheroid with N layers, a stratified spheroid with the same eccentricities, as well as confocal layered spheroids are also explicitly written down. As an application, we have numerically estimated planet Earth's outer and inner cores' ellipticities to be _o=1/413.318 and _i=1/424.616, respectively. These Earth's ellipticities values are in good agreement with those found in the literature.     

A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.