平面对偶图哈密顿性的一个充分条件

提出了平面单图的对偶图是哈密顿图的一个充分条件     

关于位势井及其对强阻尼非线性波动方程的应用

本文研究强阻尼非线性波动方程的初边值问题其中f(u)u≥0.首先用新的方法再次得到了位势井深度d的值,并首次得到了位势井内外结构.而后用位势井方法得到了问题的整体弱解,整体强解的存在性.最后证明了位势井W及井外集合V在问题(1)-(3)的流之下的不变性.     

The effect of evanescent wave modes on scattering and near-trapping

The effect of evanescent modes on the scattering and near-trappingof small-amplitude waves over axisymmetric topography is investigated.A two-stage numerical implementation, which facilitates an examinationof the resonant frequencies associated with near-trapping, isdeveloped. This is achieved in the latter stage of the procedureby dealing with the progressing and decaying waves separately. Numerical results are given for a selection of bed shapes, andit is found that the evanescent waves can have a significanteffect on scattering. Numerical evidence is found that, forthe selection of bed profiles considered, no new resonant frequenciesare introduced by the inclusion of the decaying wave components,but that the inclusion of these decaying waves does improveprevious approximations to resonant frequencies.     

Parameterized families of finite difference schemes for the wave equation

This article is devoted to an analysis of simple families of finite difference schemes for the wave equation. These families are dependent on several free parameters, and methods for obtaining stability bounds as a function of these parameters are discussed in detail. Access to explicit stability bounds such as those derived here may, it is hoped, lead to optimization techniques for so‐called spectral‐like methods, which are difference schemes dependent on many free parameters (and for which maximizing the order of accuracy may not be the defining criterion). Though the focus is on schemes for the wave equation in one dimension, the analysis techniques are extended to two dimensions; implicit schemes such as ADI methods are examined in detail. Numerical results are presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 463–480, 2004.     

A positivity‐preserving nonstandard finite difference scheme for the damped wave equation

A positivity‐preserving nonstandard finite difference scheme is constructed to solve an initial‐boundary value problem involving heat transfer described by the Maxwell‐Cattaneo thermal conduction law, i.e., a modified form of the classical Fourier flux relation. The resulting heat transport equation is the damped wave equation, a PDE of hyperbolic type. In addition, exact analytical solutions are given, special cases are mentioned, and it is noted that the positivity condition is equivalent to the usual linear stability criteria. Finally, solution profiles are plotted and possible extensions to a delayed diffusion equation and nonlinear reaction‐diffusion systems are discussed. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.     

Methods for wave equation prestack depth migration and numerical experiments

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical re-     

Physics of interferometric gravitational wave detectors

The Caltech-MIT joint LIGO project is operating three long-baseline interferometers (one of 2 km and two of 4 km) in order to unambiguously measure the infinitesimal displacements of isolated test masses which convey the signature of gravitational waves from astrophysical sources. An interferometric gravitational wave detector like LIGO is a complex, non-linear, coupled, dynamic system. This article summarizes various interesting design characteristics of these detectors and techniques that were implemented in order to reach and maintain its operating condition. Specifically, the following topics are discussed: (i) length sensing and control, (ii) alignment sensing and control and (iii) thermal lensing which changes the performance and operating point of the interferometer as the input power to LIGO is increased.     

Application of finite difference method adopted in fluid mechanics to sound propagation in ducts

Researches on sound propagation problems in ducts done by the author and other investigators in recent years are briefly discussed in this paper. The finite difference method used in fluid mechanics is used for solving these problems thus presenting an aspect of the development of research work in this field at home and abroad.The project supported by National Natural Science Foundation of China.     

Evanescent wave infrared chemical sensor possessing a sulfonated sensing phase for the selective detection of arginine in biological fluids

This paper describes a new infrared (IR) sensing scheme for the determination of arginine (Arg). In this method, the surface of an IR evanescent wave sensing element was modified with sulfonic acid groups to selectively interact with Arg through specific interactions with its guanidine moiety. The sulfonated sensing phase was prepared using a two-layer modification approach. To demonstrate that this assembly could be used for selective infrared sensing, a large number of amino acids were subjected to analysis. Although the sulfonate groups on the surface of the sensing element did interact selectively with the guanidine groups of Arg species, lysine and histidine units caused some interference; this problem could be minimized because of the unique IR absorption bands of the guanidine moiety of Arg. To optimize the detection conditions, we studied the effects of both the pH and the composition of the polymer. The most intense signal was obtained at pH 9. We observed different adsorption rates for the detection of Arg at different values of pH, which we attribute to changes in the accessibility of the analytes to the pore structures of the sensing phase. The composition of the base polymer was also optimized; 60% PVBC (w/w) provided a water-stable, sensitive phase for the detection of Arg in aqueous solution. Under the optimized conditions, we obtained a linear range of detection up to 0.1 mM with a detection limit of ca. 5 μM.     

慢波介质自由电子激光器

本文采用一维流体模型导出了慢波介质自由电子激光器的线性色散方程,建立了电子和波相互作用的同向回旋同步机理和反向回旋同步机理.