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INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

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Acta Mathematica Scientia 2011年第1期31卷 15-21页

作者：徐桂香范佳 institute of applied{2. and computational mathematics School of mathematics and Systems Science Beihang University LIMB of the Ministry of Education

In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz estimate that was originally introduced in [5].

关键词： Scattering theory Hartree equation wave operators asymptotic completeness

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science China mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2.? & SHI ZhongCi 1 1 State Key Laboratory of Scientific and Engineering Computing, institute of computational{2. and Scientific/Engineering Computing, Academy of{2. and Systems Science, Chinese Academy of Sciences, beijing 100190, China 2.Key Laboratory of{2. and applied{2. (Peking University), Ministry of Education and School of Mathematical Sciences, Peking University, beijing 100871, China 3 Graduate University of Chinese Academy of Sciences, beijing 100190, China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Graduate University of Chinese Academy of Sciences Beijing China Key Laboratory of mathematics and applied mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

Numerical and experimental investigation of the fracture behavior of shock loaded alumina

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Science China(physics,Mechanics & Astronomy) 2010年第2期53卷 244-252页

作者： REN HuiLan1,SHU XueFeng2.& LI Ping3 1 State Key Laboratory of Explosion Science and Technology,beijing institute of Technology,beijing 100081,China 2.institute of applied Mechanics and Biomedical Engineering,Taiyuan University of Technology,Taiyuan 03002.,China 3 Labroratory for Shock Wave and Detonation physics Research,institute of Fluid physics,CAEP,Mianyang 610059,China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing China institute of applied Mechanics and Biomedical Engineering Taiyuan University of Technology Taiyuan China Labroratory for Shock Wave and Detonation physics Research Institute of Fluid Physics CAEP Mianyang China

Plate impact expeiments are conducted to investigate the dynamic behavior of alumina by using one stage light gas gun. A ve-locity interferometer system for reflectors (VISAR) is used to obtain Hugoniot elastic limit and the free surface velocity profile,which consists of an elastic wave followed immediately by a dispersive inelastic wave. The stress histories under different impact velocities are measured by in-material manganin gauges. Based on the experimental data a Hugoniot curve is fitted,which shows the compressive characteristics that alumina changes typically from elastic to "plastic" ,and under higher pressure it will be transferred to similar-fluid state. The turning point of the Hugoniot curve from a high pressure region to a low pressure region is about 11.4 GPa. The fracture process of alumina is simulated by way of finite element code. After the analysis of the fracture mechanism,the numerical results show an important role played by the nucleation and the growth of the cracks in the macro-scopic fracture of the alumina target. The numerical predictions of stress histories are compared with the experimental results,which indicates consistency between them.

关键词： plate impact experiment hugoniot curve fracture characteristics numerical simulation

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波导自由电子激光带能散度非定态增益

中国激光 1996年第10期23卷 888-892页

作者：束小建北京应用物理与计算数学研究所863

推导了带能散度的波导自由电子激光高、低两共振频率支的非定态增益解析公式．给出了近似显式公式，与数值模拟结果符合很好。从所得增益脉冲分布．估算了克服呆滞效应所需腔长失谐值，在时空框架内解释了自锁模机制。

关键词：自由电子激光波导增益定态

Well-posedness and Global Attractors for the Burgers-Ginzburg-Landau Equations

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 579-588页

作者： Bo-ling Guo, Hai-yang HuangCenter of Nonlinear Studies, institute of applied{2. and computational mathematics. P.O. Box 8009. beijing 100088, ChinaDepartment of mathematics. beijing Normal University, beijing 100875, China Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 Department of mathematics Beijing Normal University 北京 100875

In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions.

关键词： Burger-Ginzbur-Landau equations Mild solution Hausdorff and fractal dimensions. Global attractor

Application of asymptotic waveform approximation technique to hybrid FE/BI method for 3D scattering

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Science in China(Series F) 2007年第1期50卷 124-134页

作者： PENG Zhen1,2.3 & SHENG XinQing2.1 institute of Electronics, Chinese Academy of Sciences, beijing 100080, China 2.Department of Electronic Engineering,{2. institute of Technology,{2. 100081, China 3 Graduated University of Chinese Academy of Sciences,{2. 100039, China institute of Electronics Chinese Academy of Sciences Beijing China Department of Electronic Engineering Beijing Institute of Technology Beijing China Graduated University of Chinese Academy of Sciences Beijing China

The asymptotic waveform evaluation （AWE） technique is a rational function approximation method in computational mathemetics, which is used in many appllcations in computational electromagnetlca. In this paper, the performance of the AWE technique in conjunction with hybrid finite element/boundary integral （FE/BI） method is firstly Inveetlgeted. The formuletlon of the AWE{2. in hybrid FE/BI method is given in detail. The characteristic implementation of the application of the AWE to the hybrid FE/BI method is discussed. Numarlcel results demonstrate that the AWE technique can greatly speed up the hybrid FE/BI method to acquire wide-band and wide-angle backecatter radar-cross-section （RCS） by complex targets.

关键词： hybrid FE/BI AWE electromagnetic scattering RCS

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 421-432页

作者： SHU BIN (institute of applied{2. & physics, Shanghai Maritime University, Shanghai 2.0135, China.) institute of applied{2. and physics Shanghai Maritime University Shanghai 200135 China

In [2.], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies. Some reduction properties are obtained. For graded Cartan type Lie algebras the author determines the first Lie-cohomology groups and the first generalized restricted cohomology groups with the coefficients in the highest weight modules from which all irreducible generalized restricted modules are derived.

关键词： Generalized restricted Lie algebras Generalized restricted Cohomology Lie algebras of Cartan type

The characteristic spectral lines of target atoms in the impact of^(40)Ar^(q+)ions on metal surfaces

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Science China(physics,Mechanics & Astronomy) 2004年第6期47卷 729-736页

作者： ZHANG Xiao’an1,2.ZHAO Yongtao1,2.LI Fuli1,YANG Zhihu2.XIAO Guoqing2.& ZHAN Wenlong2.1.Department of applied physics,Xi’an Jiaotong University,Xi’an 710049,China 2.{2. of Modern physics,Chinese Academy of Sciences,Lanzhou 730000,China Department of applied physics Xi'an Jiaotong University Xi'an 710049 China institute of Modern physics Chinese Academy of Sciences Lanzhou 730000 China

We report the measured results of the 2.0 nm—1000 nm characteristic spectral lines of target atoms when highly charged ions40Ar q+(6≤q≤14) with the same kinetic energy and40Ar6+ with different kinetic energies are incident upon Al, Ti, Ni, Ta and Au surfaces, respectively. The results for12.Xe6+,12.Xe10+ and12.Xe15+ with the same kinetic energy (150 keV) incident upon a Ta surface are also reported. These results show that when the projectile and target are properly selected (40Ar12. impinges on Al,12.Xe6+ impinges on Ta), the spectral intensity of characteristic spectral lines of the target atom is effectively enhanced, and is not strongly dependent on the kinetic energy of the incident ions.

关键词： highly charged ion, hollow atom, characteristic spectrum, spectral intensity.

Stability of Travelling Wave Solutions of the Derivative Ginzburg-Landau Equations1,2

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Communications in Nonlinear Science and Numerical Simulation 1997年第3期 20-26页

作者： Boling Guo, Bainian Lu , Guihua Wan (Laboratory of computational physics, Center for Nonlinear Studies,{2. of applied physics and computational mathematics, beijing, 100088, P.R. China) (institute of computational and App

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关键词： Ginzburg Landau equation travelling wave solution stability Chern’s number unstable augmented bundle.