The Relegation Algorithm

The relegation algorithm extends the method of normalization by Lie transformations. Given a Hamiltonian that is a power series = ₀+ ₁+ ... of a small parameter , normalization constructs a map which converts the principal part ₀into an integral of the transformed system — relegation does the same for an arbitrary function [G]. If the Lie derivative induced by [G] is semi-simple, a double recursion produces the generator of the relegating transformation. The relegation algorithm is illustrated with an elementary example borrowed from galactic dynamics; the exercise serves as a standard against which to test software implementations. Relegation is also applied to the more substantial example of a Keplerian system perturbed by radiation pressure emanating from a rotating source.This revised version was published online in October 2005 with corrections to the Cover Date.     

边坡岩体块体稳定性分析系统的开发与研究

提出了复杂形态块体几何建模的切割法, 在此基础上, 对石根华等人提出的块体理论作了改进和完善。并基于Windows操作平台, 开发了一套实用方便、实用的边坡岩体块体稳定性分析系统。经大量的实例 (例如三峡工程船闸高边坡 )检验结果表明, 该系统可以作为对边坡中复杂形状块体稳定性进行现场快速评价的实用工具。     

Numerical simulations of katabatic jumps in coats land,Antartica

A non-hydrostatic numerical model, the Regional Atmospheric Modeling System (RAMS), has been used to investigate the development of katabatic jumps in Coats Land, Antarctica. In the control run with a 5 m s^-1downslope directed initial wind, a katabatic jump develops near the foot of the idealized slope. The jump is manifested as a rapid deceleration of the downslope flow and a change from supercritical to subcritical flow, in a hydraulic sense, i.e., the Froude number (Fr) of the flow changes from Fr > 1 to Fr> 1. Results from sensitivity experiments show that an increase in the upstream flow rate strengthens the jump, while an increase in the downstream inversion-layer depth results in a retreat of the jump. Hydraulic theory and Bernoulli's theorem have been used to explain the surface pressure change across the jump. It is found that hydraulic theory always underestimates the surface pressure change, while Bernoulli's theorem provides a satisfactory estimation. An analysis of the downs balance for the katabatic jump indicates that the important forces are those related to the pressure gradient, advection and, to a lesser extent, the turbulent momentum divergence. The development of katabatic jumps can be divided into two phases. In phase I, the t gradient force is nearly balanced by advection, while in phase II, the pressure gradient force is counterbalanced by turbulent momentum divergence. The upslope pressure gradient force associated with a pool of cold air over the ice shelf facilitates the formation of the katabatic jump.     

各向异性半空间上方垂直磁偶极子电磁场的球面波展开式

文中推导出单轴各向异性媒质半空间上方垂直磁偶极源电磁场的精确解析表达式. 应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式. 该展开式数学物理意义明显，并且不受场点和源点的位置、媒质的物性参数和频率等条件的限制. 利用本文的结果可十分方便地计算和分析任意场点处的电磁场分布.     

计算机图形软件编制地图的探讨

阐述了利用Coreldraw8．0图形软件来完成《连云港市市区图》的设计和具体编制的方法，利用Coreldraw8．0图形软件的特性来提高制图效率、成图质量。结合在地图编制工作中遇到的问题，对计算机制图和传统地图理论的结合、发展提出一些看法。     

High-resolution structures of the Landers fault zone inferred from aftershock waveform data

High-frequency body waves recorded by a temporary seismic array across the surface rupture trace of the 1992 Landers, California, earthquake were used to determine fault-zone structures down to the seismogenic depth. We first developed a technique to use generalized ray theory to compute synthetic seismograms for arbitrarily oriented tabular low-velocity fault-zone models. We then generated synthetic waveform record sections of a linear array across a vertical fault zone. They show that both arrival times and waveforms of P and S waves vary systematically across the fault due to transmissions and reflections from boundaries of the low-velocity fault zone. The waveform characteristics and arrival-time patterns in the record sections allow us to locate the boundaries of the fault zone and to determine its P - and S -wave velocities independently as well as its depth extent. Therefore, the trade-off between the fault-zone width and velocities can be avoided. Applying the method to the Landers waveform data reveals a low-velocity zone with a width of 270–360 m and a 35–60 per cent reduction in P and S velocities relative to the host rock. The analysis suggests that the low-velocity zone extends to a depth of ∼7 km. The western boundary of the low-velocity zone coincides with the observed main surface rupture trace.     

Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Utility Efficient Frontier: An Application in the Oil and Gas Industry

Current practice shows that the use of portfolio and utility theory is very low among petroleum companies. This article advocates the use of both portfolio theory and utility theory as decision-making tools to improve performance of oil and gas companies. We introduce a model that can be practically used and applied in the oil and gas industry. This model generates an optimized, efficient portfolio and, at the same time, enables the decision maker to incorporate his risk attitude and policy. This can only be done by combining both the portfolio theory and utility theory through an approach called the utility mean-variance model. A typical oil portfolio optimization problem is investigated by applying both portfolio and utility theories. Through the utility mean-variance model, an efficient frontier that captures decision maker risk attitude is achieved.