任一力学量■的矩阵元Fmn的微扰近似计算

本文以能量和波函数的各级微扰近似的基态展开式为基础,推导出任一力学量的矩阵元F_(mn)的各级微扰近似表示式。并且指出只要构成能量展式的级数收敛很快,满足能够应用微扰的条件,那么对于任一力学量F的微扰计算,只要计算矩阵元F_(mn)的前二级近似就已足够精确。     

ANALYSES OF THE DYNAMIC EFFECTS ON WINTER CIRCULATION OF THE TWO MAIN MOUNTAINS IN THE NORTHERN HEMISPHERE——Ⅱ.VERTICAL PROPAGATION OF PLANETARY WAVES

A linear,hemispheric and stationary spectral model with multilayers in the vertical was employed to simulate thevertical propagation of waves triggered by mountains.Results show that,in cooperation with the East Asia zonal meanflow,Tibetan Plateau can excite a strong wavenumber 1 perturbation in the stratosphere with its ridge and trough lo-cated over the Pacific and Atlantic Oceans respectively.On the other hand,the stratospheric wavenumber 1 perturbationcaused by the mechanical forcing of the Rocky Mountains in cooperation with the North America zonal mean flow isvery weak.Calculations from observational data of the vertical profile of critical wavenumber for vertically propagatingwaves imply that the tropospheric wavenumber 1 perturbation can hardly penetrate the North America tropopause up-wards,whereas it can freely propagate through the East Asia tropopause into the stratosphere.Two-dimensional E-Pcross-sections obtained from both observational data and simulated results also demonstrate that waves excited by theRocky Mountains are refracted towards low latitudes in the troposphere during their upward propagation:whereas,inaddition to the above mentioned equatorward leaning branch,the wavenumber 1 and 2 planetary waves excited by theTibetan Plateau possess another branch which is refracted to high latitudes during upward propagation and penetratesthe tropopause into the stratosphere.It is therefore concluded that the difference in the horizontal and vertical wavepropagations in the two hemispheres is a result of the different dynamical forcing induced by the two main mountains inthe Northern Hemisphere.     

Propagation of Extremely Low Frequency Waves Through the Ionosphere

The propagation features of extremely low frequency electromagnetic waves through the multicomponent ionospheric plasma are studied. It is shown that at relatively lower frequencies refractive index for right hand mode is higher than the left-hand mode, which is reversed at higher frequencies. The thermal temperature of plasma particle causes decrease in phase and group velocities of both right and left-hand modes. The crossover frequencies for different plasma models are computed and variation with ion concentration and thermal velocity is studied. Explicit expression for group velocity and travel time has been derived and studied numerically. Finally, we have presented simulation of the ion whistler spectrograms for Hydrogen, Helium and Oxygen ions present in the ionospheric plasma. The results are compared with the experimentally detected hydrogen and helium ion whistlers. The importance of the present study in the exploration of ionospheric plasma is illustrated.     

地形作用下有限振幅Rossby波的稳定性分析

本文用微分方程定性理论方法分析了地形对有限振幅Rossby波的稳定性影响。结果表明:地形北坡有利于波动出现不稳定,南坡使波动稳定;西坡使导式波动不稳定但使曳式波动稳定,东坡使导式波动稳定但使曳式波动不稳定。     

Source signature and elastic waves in a half‐space under a momentary shear line impulse

The transient deformation of an elastic half‐space under a line‐concentrated impulsive vector shear load applied momentarily is disclosed in this paper. While in an earlier work, the author gave an analytical–numerical method for the solution to this transient boundary‐value problem, here, the resultant response of the half‐space is presented and interpreted. In particular, a probe is set up for the kinematics of the source signature and wave fronts, both explicitly revealed in the strained half‐space by the solution method. The source signature is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Fourteen wave fronts exist behind the precursor shear wave S: four concentric cylindrical, eight plane, and two relativistic cylindrical initiated at propagating centres that are located on the stationary boundaries of the solution domain. A snapshot of the stressed half‐space reveals that none of the 14 wave fronts fully extend laterally. Instead, each is enclosed within point bounds. These wave arresting points and the two propagating centres of the relativistic waves constitute the source signature. The obtained 14 wave fronts are further combined into 11 disparate wave fronts that are grouped into four categories: an axis of symmetry wave—so named here by reason of being a wave front that is contiguous to the axis of symmetry, three body waves, five surface waves and two inhibitor waves—so named here by reason that beyond them the material motion dies out. Of the three body waves, the first is an unloading shear wave, the second is a diffracted wave and the third is a reflected longitudinal two‐branch wave. Of the two inhibitor waves, the first is a two‐joint relativistic wave, while the second is a two‐branch wave. The wave system, however, is not the same for all the dependent variables; a wave front that appears in the behaviour of one dependent variable may not exist in the behaviour of another. It is evident from this work that Saint–Venant's principle for wave propagation problems cannot be formulated. Therefore, the above results are valid for the particular proposed model for the momentary line‐concentrated shear load. The formulation of the source signature, the wave system, and their role in the half‐space transient deformation are presented here. Copyright © 2003 John Wiley & Sons, Ltd.