解非光滑方程组的Newton-GMRES算法

给出了求解非光滑方程组的Newton—GMRES迭代法。该方法在求解半光滑方程组时，不需要计算广义Jacobi矩阵，同时使求解相应广义Newton方程组也变得容易。尤其对于大型问题，该方法特别适用。数值例子显示了这种方法的有效性。     

摆线型大位移井剖面设计的数值计算

摆线型大位移井轨道由“直井段—圆弧井段—摆线井段—稳斜井段”构成,与其他类型的大位移井轨道相比,摆线型大位移井具有最小的或很小的摩阻和摩阻力矩。摆线型大位移井轨道设计问题归结为求解一个二元方程组,当未知设计参数为摆线井段初始井斜角或稳斜井段井斜角时,该方程组为非线性方程组,没有解析解。通过数学变换和化简,得到了等价的三角函数方程,根据区间搜索和二分法提出了求该三角函数方程近似解的数值迭代算法。算例表明,该算法具有很好的迭代稳定性,计算精度高、速度快。新算法可用于大位移井轨道设计的计算机软件开发,对于提高软件的适用性和稳定性具有较大的帮助。     

层状地基中单桩负摩擦问题积分方程解法

利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去,对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换,就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明,桩侧剪力和孔压分层明显。     

竖向简谐荷载下二维层状饱和地基的解析层元解

基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。     

弹性地基板的分析简化模型

将弹性半空间地基受任意竖向荷载作用下的静力位移积分变换解与弹性半空间地基上四边自由矩形板受任意竖向荷载作用的弯曲解析解相结合,建立了求解板下地基位移的方法。对一些算例进行大量数值计算分析,得出弹性半空间地基上四边自由矩形板板下地基水平位移和竖向位移的分布规律;并基于该位移分布规律,提出地基位移沿深度按一定的函数关系变化的假设,考虑板下地基水平位移,利用板地基系统的总势能最小原理,通过复杂的变分运算,得出弹性地基板的简化模型。在不考虑板下地基水平位移时,该模型退化成双参数地基模型,并给出了求解其上四边自由矩形板的近似边界条件。     

大区域地下水模拟的预优并行GMRES(m)算法研究

大区域研究区由于涉及范围大、水文地质参数复杂多变,一直是进行地下水数值模拟的热点和难点。针对大区域地下水模拟的特点,在MPI环境中对Krylov子空间GMRES(m)算法的并行性进行分析,提出基于区域分解法的并行实现策略,并对不同的预条件子的加速效果进行比较。数值实验结果表明:并行GMRES(m)算法在求解大区域三维地下水模型时可以显著的加快求解速度,且具有较好的可扩展性。另外,Jacobi预条件子与GMRES算法的组合具有更优的加速比和执行效率,是一种求解大型化、复杂化地下水水流问题的可行方案。     

成层地基在轴对称荷载下的稳态振动分析

基于Biot动力固结方程,考虑了土体和水体的惯性力以及水-土耦合作用的影响,采用Hankel积分变换求解耦联合方程组,得到动荷载下饱和土Lamb问题的解答。根据下边界为不透水基岩的边界条件,获得了地基表面作用圆形轴对称周期荷载时土层应力、位移等的一般积分形式解,并利用矩阵传递法完成了对多层地基和Gibson地基的计算。通过算例研究了层厚和激振频率等对竖向位移的影响。     

杂交边界点法求解带自由面的渗流问题

将杂交边界点法与迭代法相结合,求解有自由面的渗流问题。杂交边界点法基于杂交位移变分原理和移动最小二乘近似,利用基本解插值域内的场函数,而边界上的变量则用移动最小二乘近似,是一种纯边界类型的无网格方法。利用该方法只需在边界上布点而不需要划分任何网格的特性,先假定自由面的初始位置,再进行迭代求解。数值算例表明,该方法精度较高、计算量较小,适合于求解各种具有自由面的渗流问题。     

基坑开挖诱发周围土体水平移动的解析解

基于位移-位移平面应变边值问题,从理论上求解基坑挡墙水平变位诱发墙后周围土体水平移动。通过镜像映射法求得了挡墙平移与绕墙趾转动等两种基本刚性挡墙位移模式下墙后周围土体水平移动的精确理论解;在土体不可压缩的特定条件下,将该理论解与经典的汇-源理论解进行了对比验证。理论分析表明,周围土体水平移动主要取决于挡墙位移模式及位移大小,与地基土的变形模量无关。针对不可压缩土体,对比该精确解与汇-源理论近似解的理论预测发现,两种理论方法求得的周围土体水平移动规律一致,但在挡墙最大变位处相邻范围内,汇-源理论求得的土体水平位移偏小,在挡墙变位较小处相邻范围内,汇-源理论求得的土体水平位移偏大。     

直-增-稳剖面设计问题的解析解

使用无量纲化方法对设计方程组进行了改写,新的无量纲化设计方程组有利于充分利用三角函数公式求解析解,所得到的解析解计算公式具有简洁的数学形式。将设计方程组求解问题分成两类,对于已知最大井斜角的第Ⅰ类问题,使用线性代数解方程组的克莱默法则直接就可以得出解析解。最大井斜角为未知数的第Ⅱ类问题,使用三角函数公式进行化简,得到形式简单、统一的解析解公式,避免了使用半角公式所带来的解析解计算公式的复杂性。所使用无量纲化方法具有一定的普适性,可以用于解决其他类型的二维剖面设计问题。     

Galaxies with rows

The results of a search for galaxies with straight structural elements, usually spiral-arm rows (“rows” in the terminology of Vorontsov-Vel'yaminov), are reported. The list of galaxies that possess (or probably possess) such rows includes about 200 objects, of which about 70% are brighter than 14^m. On the whole, galaxies with rows make up 6–8% of all spiral galaxies with well-developed spiral patterns. Most galaxies with rows are gas-rich Sbc-Scd spirals. The fraction of interacting galaxies among them is appreciably higher than among galaxies without rows. Earlier conclusions that, as a rule, the lengths of rows are similar to their galactocentric distances and that the angles between adjacent rows are concentrated near 120° are confirmed. It is concluded that the rows must be transient hydrodynamic structures that develop in normal galaxies.     

Landscaping with waste

For centuries back, man has searched for and utilised geological material resources for many different purposes. These efforts have left many, large wounds or “eyesores” in bedrock and soil strata, that have destroyed the appearance of the original landscape, and which now often serve as waste dumps and scrap sites. Worked-out gravel and sand pits, as well as extinct quarries and open-pit mineral mines, can extend over wide areas of land and reach considerable depths. Depths which subsequently have become particularly attractive as waste storage sites, especially when these offer short transport distances to suppliers in major, built-up areas and communities.

This paper gives some examples as to how Stockholm has replaced worked-out overburden and rock masses from eskers and rock strata with waste masses, simultaneously restoring land formation into its original condition through landscaping. Specific engineering-geological survey methods, control systems, as well as risk and sequel analyses, relating to long-term interplay between rock, soil strata and groundwater, with particular consideration to surface construction and property development planning and isostatic uplift, will be presented.     

Living with volcanoes

The 1990s were designated the International Decade of Natural Disaster Reduction (IDNDR) by the United Nations and considerable research effort has gone into achieving a better understanding of volcanic processes and public understanding of volcanic phenomena. Some eruptions have been predicted successfully and thousands of lives have been saved through evacuation and well co-ordinated aid programmes.     

An elliptic problem with integral constraints with application to large-scale geophysical flows

We present a weak formulation of a non-standard elliptic equation whose boundary values are determined in part by integral relations. Existence and uniqueness of its solution are proved, and a finite element discretization is described, analyzed, and implemented on a test problem. The equation is a generalization of one that is solved during integration of the three-dimensional Quasigeostrophic equations, which model large-scale rotating stratified flows, where the integral constraints represent conservation of physical properties.     

与碳酸岩共生的霓长岩

本文归纳总结了从20世纪60年代以来国外与碳酸岩有关的霓长岩的相关研究成果,主要涉及了岩石学、矿物学和地球化学等方面。与碳酸岩有关的霓长岩是碳酸岩侵位时对围岩交代作用产生的岩石,其主要组成矿物为碱性铁镁矿物和碱性长石等。根据霓长岩与碳酸岩的空间关系、其显微结构及矿物共生组合,可将霓长岩划分为低级、中级和高级不同类型。霓长岩的矿物学研究侧重于对其矿物组成及矿物化学成分的研究,据此可了解交代流体的性质、交代作用时的物理条件并追索流体的来源。在霓长岩化过程中,初生碳酸岩浆逸出的大量碱金属和挥发分进入了围岩中形成霓长岩,因此,通过对霓长岩元素和同位素地球化学的研究,有助于理解初生碳酸岩浆的性质和其地幔来源区特征。     

Urban analysis with GIS

This paper discusses how GIS (Geographic Information System) can contribute to the research field of urban analysis. The purpose of urban analysis is to explain the processes of spatial distributions in urban areas. For this purpose, urban analysts often need to manipulate large amounts of spatial data. This is the reason why urban analysis cannot advance without GIS. Analysts can visualize urban affairs using GIS and find the processes of spatial distributions. For example, in this paper, land use distributions in Nagoya City, Japan are visually analyzed with ArcView GIS. This analysis demonstrates that GIS can contribute to urban analysis. After this analysis, future work is discussed based on the reviews of recent studies on urban analysis using GIS. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental evaluation of biases associated with sampling estuarine fishes with seines

Beach seines are widely used to estimate the density and species richness of fishes in estuaries. We evaluated the causes and extent of bias in estimates from seines using a series of field experiments in small estuaries in southern California, USA. Seining in spatially paired areas that were either enclosed by block nets or not, revealed that seines used without block nets und erestimated density by more than 4-fold and species richness by more than 2-fold relative to blocked areas. Seining in paired blocked areas with seines of two lengths revealed that net length affected estimates of density, but not species richness; a 7.6-m long seine produced 1.6-fold higher estimates of total density than did a 15.2-m long seine due to increased catches of demersal fishes, but not midwater species. Paired sampling in blocked areas also revealed that many fishes initially evaded capture by the seine. Estimates of density but not species richness were significantly higher in areas through which a seine was swept 5 times compared to once. This was due to higher catches of demersal fishes but not midwater fishes in areas seined 5 times. Repeated seining through blocked areas revealed that the vast majority (90% or more) of species and individuals of midwater fishes were captured within the first 5 sweeps, compared to only about 50% of the individuals of demersal species. A mark-recapture study in blocked areas revealed lower probabilities of capture for demersal species relative to midwater species.     

Kriging with Inequality Constraints

A Gaussian random field with an unknown linear trend for the mean is considered. Methods for obtaining the distribution of the trend coefficients given exact data and inequality constraints are established. Moreover, the conditional distribution for the random field at any location is calculated so that predictions using e.g. the expectation, the mode, or the median can be evaluated and prediction error estimates using quantiles or variance can be obtained. Conditional simulation techniques are also provided.     

Conditional Simulation with Patterns

An entirely new approach to stochastic simulation is proposed through the direct simulation of patterns. Unlike pixel-based (single grid cells) or object-based stochastic simulation, pattern-based simulation simulates by pasting patterns directly onto the simulation grid. A pattern is a multi-pixel configuration identifying a meaningful entity (a puzzle piece) of the underlying spatial continuity. The methodology relies on the use of a training image from which the pattern set (database) is extracted. The use of training images is not new. The concept of a training image is extensively used in simulating Markov random fields or for sequentially simulating structures using multiple-point statistics. Both these approaches rely on extracting statistics from the training image, then reproducing these statistics in multiple stochastic realizations, at the same time conditioning to any available data. The proposed approach does not rely, explicitly, on either a statistical or probabilistic methodology. Instead, a sequential simulation method is proposed that borrows heavily from the pattern recognition literature and simulates by pasting at each visited location along a random path a pattern that is compatible with the available local data and any previously simulated patterns. This paper discusses the various implementation details to accomplish this idea. Several 2D illustrative as well as realistic and complex 3D examples are presented to showcase the versatility of the proposed algorithm.