二次特征值问题的最佳向后扰动分析

二次特征值问题 (QEP)的主要的求解方法之一是转化为广义特征值问题 (GEP) ,然后用求解广义特征值的方法 (比如 QZ方法 )求解。本文研究由此获得的计算解的范数意义下的最佳向后扰动分析 ,所得结果是 Tisseur最近所得结果的加强。     

Reflection of waves from the boundary of a random elastic semi-infinite medium

In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity , where measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ². The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

Low-low satellite-to-satellite tracking: a comparison between analytical linear orbit perturbation theory and numerical integration

Low-low satellite-to-satellite tracking (ll-SST) range-rate observations have been predicted by two methods: one based on a linear perturbation theory in combination with the Hill equations, and one based on solving the equations of motion of two low-flying satellites by numerical integration. The two methods produce almost equivalent Fourier spectra of the range-rate observations after properly taking into account a few resonant terms. For a typical GRACE-type configuration, where the two satellites trail each other at a distance of 300 km at an altitude of 460 km, and in the presence of the EGM96 gravity field model, complete to spherical harmonic degree and order 70, the agreement between the Fourier spectra is about 1 mm/s compared to a root-mean-square (RMS) value of more than 220 mm/s for the range-rate signal. The discrepancy of 1 mm/s can be reduced significantly when not taking into account perturbations caused by the J₂ term. Excluding the J₂ term, the agreement between the two methods improves to 0.4 mm/s compared to a RMS value of 6 mm/s for the range-rate signal. These values are 0.01 and 2.3 mm/s when ignoring the spectrum for frequencies below two cycles per orbital revolution, reducing the discrepancy even further to about 0.5% of the signal. The selected linear perturbation theory is thus capable of modeling gravity field induced range-rate observations with very high precision for a large part of the spectrum.     

斜交型不稳定谱点分布侧半圆定理及其增长率上界的估计

本对斜交型扰动不稳定谱点的分布做了理论分析，得到了该谱点分布的半圆定理一该谱点分布在复一面上以原点为圆心以R0为半径的上半平面上，同时还对该不稳定增长率的上界作了估计。发现水平永度越小，模式顶越高则该估计值越大；垂直风切变的增大和纬度的增高对该增长率的增大有正贡献；当层结稳定度减小时，最大增长率随相对最大增长率得增大而减小。     

Determination of Area-Averaged Water Vapour Fluxes with Large Aperture and Radio Wave Scintillometers over a Heterogeneous Surface – Flevoland Field Experiment

A large aperture scintillometer (LAS) andradio wave scintillometer (RWS)were installed over a heterogeneous areato test the applicability of the scintillation method.The heterogeneity in the area, whichconsisted of many plots, was mainly caused bydifferences in thermal properties ofthe crops; the variations in theaerodynamic roughness lengthwere small. The water vapour fluxesderived from the combined LAS-RWSsystem, also known as the two-wavelengthmethod, agreed fairly well with the aggregatedwater vapour fluxes derived from in-situeddy covariance measurements. The water vapourfluxes derived from a stand-alone LASare also presented. It was found that a single LASand an estimate of the area averagedavailable energy (using a simple parameterisationscheme) can provide also reasonablearea-averaged water vapour fluxes.     

A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

有限弹性变形地壳中的地震波

地壳由半无限大的基岩上一层厚度为H^-的表土层组成，入射地震波为垂直的SH波，产生水平地面运动。当浅源大地震发生时，在极震区以外行波传播产生地面运动将使地壳介质有非线性的有限弹性变形。用小参数摄动法使非线性控制方程为线性化的小参数各阶控制方程，得出头两阶线性控制方程的解析解。     

《CT理论与应用研究》杂志新刊标和地幔速度模型的说明

在《ＣＴ理论与应用研究》杂志１９９４~２００１年本杂志“刊标”的基础上,在其上方增加了象征三维体视学成像的三角形四面体的透视图;该刊标的右下侧为医学断面成像扫描仪(包括各种Ｘ－ＣＴ机与核磁共振ＭＲＩ扫描仪等);其左下侧为三维地幔速度模型和地球核的示意图,切出有两个地幔剖面,表示纵波速度二维变化的剖面。该速度剖面系根据赵大鹏教授的理论和计算方法,按照地球上的两个大圆弧做计算和绘制的彩色图,排在本期封４:第一大圆弧,从北极经西巴基斯坦(２８°Ｎ, ６４°Ｅ)到马尔代夫群岛(３°Ｎ,７３°Ｅ);第二大圆弧从马尔代夫群岛点(３°Ｎ,７３°Ｅ)连接巴布新几内亚之南点(１２°Ｓ,１５０°Ｅ),来计算两剖面速度分布并作图的结果,其具体分布参见封４的两条彩色剖面和相应的地理位置图。由于赵教授这篇论文[１]在中国国内只有很少数图书馆收藏,在Ｅｌｓｅｖｉｅｒ Ｓｃｉｅｎｃｅ的ＥＰＳＬ网站上一般人只能查到摘要,本刊对于该地幔速度模型的制作方法和所用数据资料,该模型的优越性和特征进行了叙述,他所用的地震事件数目,多达７１２８个;用于层析反演成像的震相到时数多到近一百万条。该速度如下的特点:在所采用的速度结构中,包含用几个复杂形状的地质速度界面,如莫霍面,以及下沉板块的分界