Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.

     

用于波分复用系统的多峰干涉滤光片

介绍了用于波分复用系统的多峰干涉滤光片的设计原理,提出了滤光片透射峰位置的确定方法,讨论了影响滤光片半宽度和截止度的因素,给出了滤光片的膜厚容差分析结果,表明透射率监控标准偏差在<0.5%范围内,可以得到波形良好的多峰滤光片,最后给出了实验结果.     

北京谱仪Ⅲ电磁量能器触发系统的模拟研究

利用北京谱仪Ⅲ探测器模拟和触发系统模拟程序,研究了北京谱仪Ⅲ电磁量能器的触发方案.根据物理目标设计了中性事例触发,巴巴事例判选和带电事例触发的方案,优化了各触发条件的参数,并仔细研究了对本底的排斥能力.研究了一批典型的物理道,给出了它们的触发效率,同时给出了预期的本底触发事例率.     

Rate constants for the gas‐phase reaction of CF3CF2CF2CF2CF2CHF2 with OH radicals at 250–430 K

The rate constants k₁ for the reaction of CF₃CF₂CF₂CF₂CF₂CHF₂ with OH radicals were determined by using both absolute and relative rate methods. The absolute rate constants were measured at 250–430 K using the flash photolysis–laser‐induced fluorescence (FP‐LIF) technique and the laser photolysis–laser‐induced fluorescence (LP‐LIF) technique to monitor the OH radical concentration. The relative rate constants were measured at 253–328 K in an 11.5‐dm³ reaction chamber with either CHF₂Cl or CH₂FCF₃ as a reference compound. OH radicals were produced by UV photolysis of an O₃–H₂O–He mixture at an initial pressure of 200 Torr. Ozone was continuously introduced into the reaction chamber during the UV irradiation. The k₁ (298 K) values determined by the absolute method were (1.69 ± 0.07) × 10^?15 cm³ molecule^?1 s^?1 (FP‐LIF method) and (1.72 ± 0.07) × 10^?15 cm³ molecule^?1 s^?1 (LP‐LIF method), whereas the K₁ (298 K) values determined by the relative method were (1.87 ± 0.11) × 10^?15 cm³ molecule^?1 s^?1 (CHF₂Cl reference) and (2.12 ± 0.11) × 10^?15 cm³ molecule^?1 s^?1 (CH₂FCF₃ reference). These data are in agreement with each other within the estimated experimental uncertainties. The Arrhenius rate constant determined from the kinetic data was K₁ = (4.71 ± 0.94) × 10^?13 exp[?(1630 ± 80)/T] cm³ molecule^?1 s^?1. Using kinetic data for the reaction of tropospheric CH₃CCl₃ with OH radicals [k₁ (272 K) = 6.0 × 10^?15 cm³ molecule^?1 s^?1, tropospheric lifetime of CH₃CCl₃ = 6.0 years], we estimated the tropospheric lifetime of CF₃CF₂CF₂CF₂CF₂CHF₂ through reaction with OH radicals to be 31 years. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 26–33, 2004     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

A representation of acoustic waves in unbounded domains

Compact, time‐harmonic, acoustic sources produce waves that decay too slowly to be square‐integrable on a line away from the sources. We introduce an inner product, arising directly from Green's second theorem, to form a Hilbert space of these waves and present examples of its computation.¹ © 2005 Wiley Periodicals, Inc.     

The Analysis and Improving of the Microwave Exciter in the Lower Hybrid Wave System

When we carry out lower hybrid wave heating and current driving plasma experiment at tokamak, we need mega-watt order of microwave power. The microwave signal at frequency of 2450 MHz is generated by a microwave exciter. According to the experiment＇s demands, the microwave exciter must provide output power of 1.5～ 2. 5 W with stabilized frequency and amplitude tobe used as the klystron input. Being amplified by the klystron, the microwave signal is transmitted through the transmitting system to the antenna and is emitted into the HL-2A tokamak. So we can see that the microwave exciter＇s function is very important to the lower hybrid wave heating and current driving plasma experiment.     

Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.     

Novel hexadentate imidazolium salts in the rhodium-catalyzed addition of arylboronic acids to aldehydes

Four novel hexadentate imidazolium salts were synthesized from hexakis(bromomethyl)benzene and 1-substituted imidazole. The arylation of aldehydes with arylboronic acids was effected conveniently and in high yields by a catalyst system generated in situ from these hexadentate imidazolium salts, [Rh(COD)Cl]₂ and a base.