Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

三维抛物方程Douglas交替方向隐格式的稳定性和收敛性

作者研究三维变系数抛物方程 Douglas交替方向隐格式的稳定性和收敛性。采用 H1能量估计方法 ,证明格式按离散 H1范数是绝对稳定的 ,并且收敛阶为 O(Δ t2 + h2 )     

蒸发波导环境下风浪对电磁波传播影响的数值模拟研究

蒸发波导是一种特殊的大气波导,在其中传播的电磁波信号会被陷获在近海大气层中,实现超视距传播。受海表面温度、湿度、风速、微波频率等因素的影响,海洋蒸发波导环境中的微波传播特性起伏变化很大,规律十分复杂。以往的工作主要通过计算这些气象因素对蒸发波导条件下大气折射率剖面的影响来分析它们对路径损失的作用,其结果与实验数据仍有较大差异。本文在一定的蒸发波导条件下,利用一维分形海面模型产生海面“地形”,将其作为抛物方程电磁波传播模型的边界条件进行计算,得到相应的路径损失,并与传统计算方法进行对比,分析了不同蒸发波导高度、不同频率及不同接收天线高度时的数值模拟情况,可为舰艇通信系统或者雷达系统的设计提供相应的依据。     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

Permeability Estimation with the Augmented Lagrangian Method for a Nonlinear Diffusion Equation

We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formulated as a constrained minimization problem. The parameter estimation problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the conjugate gradient method. The methodology is developed and numerical experiments with the proposed method are presented.     

Parabolic density function in sedimentary basin modelling

For modelling sedimentary basins of large thickness from their gravity anomalies, the concept of parabolic density function which explains the variation of true density contrast of the sediments with depth in such basins is introduced inBott's (1960) procedure. The analytical expression the gravity anomaly of a two-dimensional vertical prism with parabolic density contrast needed to estimate the gravity effect of the basin in modelling procedure is derived in a closed form. Two profiles of gravity anomalies, one across San Jacinto Graben, California and the other across Tucson basin, Arizona where the density of sediments is found to vary with depth are interpreted.     

MIDAS-W: a workstation-based incoherent scatter radar data acquisition system

The Millstone Hill Incoherent Scatter Data Acquisition System (MIDAS) is based on an abstract model of an incoherent scatter radar. This model is implemented in a hierarchical software system, which serves to isolate hardware and low-level software implementation details from higher levels of the system. Inherent in this is the idea that implementation details can easily be changed in response to technological advances. MIDAS is an evolutionary system, and the MIDAS hardware has, in fact, evolved while the basic software model has remained unchanged. From the earliest days of MIDAS, it was realized that some functions implemented in specialized hardware might eventually be implemented by software in a general-purpose computer. MIDAS-W is the realization of this concept. The core component of MIDAS-W is a Sun Microsystems UltraSparc 10 workstation equipped with an Ultrarad 1280 PCI bus analog to digital (A/D) converter board. In the current implementation, a 2.25 MHz intermediate frequency (IF) is bandpass sampled at 1 s intervals and these samples are multicast over a high-speed Ethernet which serves as a raw data bus. A second workstation receives the samples, converts them to filtered, decimated, complex baseband samples and computes the lag-profile matrix of the decimated samples. Overall performance is approximately ten times better than the previous MIDAS system, which utilizes a custom digital filtering module and array processor based correlator. A major advantage of MIDAS-W is its flexibility. A portable, single-workstation data acquisition system can be implemented by moving the software receiver and correlator programs to the workstation with the A/D converter. When the data samples are multicast, additional data processing systems, for example for raw data recording, can be implemented simply by adding another workstation with suitable software to the high-speed network. Testing of new data processing software is also greatly simplified, because a workstation with the new software can be added to the network without impacting the production system. MIDAS-W has been operated in parallel with the existing MIDAS-1 system to verify that incoherent scatter measurements by the two systems agree. MIDAS-W has also been used in a high-bandwidth mode to collect data on the November, 1999, Leonid meteor shower.     

近岸波浪破碎区不规则波浪的数值模拟

基于近岸不规则波浪传播的抛物型缓坡方程和两类波浪破碎能量损耗因子,对近岸波浪破碎区不规则波浪的波高分布进行了数值模拟,并结合实验结果对数值模拟结果进行了验证分析,结果表明采用两类波浪破碎能量损耗因子所模拟的破碎区波高与实测值均吻合良好,波浪破碎能量损耗因子及波浪破碎指标对破碎区波浪波高分布影响较明显。     

象山皇城海滩稳定性分析与防护对策

以浙江岬湾砂质海岸象山皇城海滩为例,运用抛物线模型,分析得出皇城海滩的冲淤演化动态,并通过历史岸线形态对比探讨皇城海塘对其的影响,最终提出防止海岸侵蚀的对策。研究结果表明,皇城海滩北部有一定的侵蚀,其平面形态还未达到静态平衡,处于不稳定状态;皇城海滩北段海塘修建得过于靠海,致使海滩最重要的泥沙补给源——后滨沙丘被阻断,甚至消失,同时大潮水位可直接淹没海塘堤脚,加上海塘前为近破波,滩面水流和泥沙运动剧烈,最终导致堤前滩面的冲刷。基于此,防止海岸侵蚀的最佳对策是在拆除、重建海滩北部部分海塘后再进行适当的海滩养护。通过对皇城海滩的稳定性研究,了解海塘建设的影响,可为浙江岬湾海滩资源的合理开发、海岸防护工程建设提供一定的科学依据。