二阶不稳定型中立型微分方程解的振动准则

改进不稳定型二阶中立型微分方程的最后结果,进一步研究该类方程解的振动条件。     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.     

重力异常垂向一阶导数的一种简便算法

利用拉格朗日插值导出了重力异常垂向一阶导数的计算公式，给出了地面以及地面之上不同高度的求导系数。该公式可以计算地面上的重力垂向一阶导数，还可以直接计算地面之上任意高度上的垂向一阶导数。鉴于该公式除系数不同外，与上延公式完全相同，因此，程序设计尤为简单。使用本公式对模型数据和实际资料进行了处理，证明了本算法的实用性。     

一种基于启发式算法的等高线局部内插方法

在基于启发式内插等高线算法的基础上提出了一种局部内插方法。首先利用Douglas-Peucker算法提取等高线的特征点,根据特征点判断等高线之间的相似性程度,找出导致等高线出现异常的特征点;然后将相似性程度很低的两条等高线自动分解为若干简单等高线再进行内插。有效地解决了局部弯曲很大、马鞍型地貌等复杂等高线的内插问题。算法已经在以Microstation为平台的数字制图系统中实现并逐渐实用化。     

基于精密星历的计算卫星位置的方法

分析了拉格朗日多项式插值算法,提出了将Neville算法实现于精密星历的插值,数值试验表明,其克服了函数插值的龙格现象,有很好的逼近效果.     

基于钻孔数据的三维地质建模与可视化研究

三维地质模型能够完整准确地表达复杂地质现象的边界条件及地质体内含的各种地质构造,直观地再现地质单元的空间展布及其相互关系,最大限度地提高地质分析的直观性和准确性,因此三维地质建模已引起地质、采矿、岩土工程等诸多领域的日益重视。笔者在综合考察多种建模方法的基础上,结合工程实践,提出了一种实用的工程地质三维建模实施方法。该方法以钻孔资料和地质剖面数据为三维地质建模的源数据,允许用户手工修正模型剖面地层分界线,从而实现对建模过程的干预和控制,克服了单纯依靠钻孔数据建模结果不精确且难以修正的问题。最后,通过一个研究实例展示了该方法的实际建模效果。     

A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a membrane to a thin steel plate), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.On leave from the Department of Physical Geography and Cartography, Comenius University, Mlynská dolina, Bratislava, Czechoslovakia.On leave from the Institute of Physics, Dúbravská cesta 9, Bratislava, Czechoslovakia.     

SPOT5影像严格几何纠正方法研究

根据SPOT卫星的成像原理和特点,讨论了对SPOT5卫星影像按共线方程法进行有控制点的几何纠正的方法,经对关中、陕北和陕南三种地形的影像纠正结果进行对比检验,证明了该方法精度达到了较高水平。