数值方程

Lasers characteristic as a shock wave drive and the advantages of KrF laser are explained. Finally, the progress at home and abroad is enumerated.In chapter two, the basic principle of the EOS study is introduced. Specially, the impedance mismatch effect of the double-layer flyer is mentioned here. It is the primary theoretical basis of this paper.In chapter three, a one-dimension, three-temperature hydrodynamic code HYADES is introduced briefly. it is used to make a qualitative analysis about how the thickness of ablator affect the flyer velocities and stability.In chapter four, the experimental setup is described.

第一章为绪论部分，简要总结了状态方程研究的历史，激光作为冲击波驱动源的特点和KrF激光的优势，以及国内外的进展情况；第二章是本工作的理论基础，讨论了冲击波物理和雨贡纽曲线测量的基本原理和方法，重点介绍了激光飞片法的特点、关键要素和双层飞片的阻抗失配效应，鉴于KrF激光短波长和长脉宽的特点，我们拟对双层飞片的特性展丌研究工作，为实测状态方程做好准备；第三章简单介绍了一维三温流体力学数值模拟程序Hyades并运用它进行了若干状态方程实验的计算和设计，进行了烧蚀层厚度对飞片速度、稳定性的影响的定性分析；第四章是实验平台描述部分，介绍了光束平滑化技术，靶的制作，条纹相机的原理和使用，系统同步控制以及光学记录速度干涉仪系统的简单原理和构成。

Laser's characteristic as a shock wave drive and the advantages of KrF laser are explained. Finally, the progress at home and abroad is enumerated.In chapter two, the basic principle of the EOS study is introduced. Specially, the impedance mismatch effect of the double-layer flyer is mentioned here. It is the primary theoretical basis of this paper.In chapter three, a one-dimension, three-temperature hydrodynamic code HYADES is introduced briefly. it is used to make a qualitative analysis about how the thickness of ablator affect the flyer velocities and stability.In chapter four, the experimental setup is described.

第一章为绪论部分，简要总结了状态方程研究的历史，激光作为冲击波驱动源的特点和KrF激光的优势，以及国内外的进展情况；第二章是本工作的理论基础，讨论了冲击波物理和雨贡纽曲线测量的基本原理和方法，重点介绍了激光飞片法的特点、关键要素和双层飞片的阻抗失配效应，鉴于KrF激光短波长和长脉宽的特点，我们拟对双层飞片的特性展丌研究工作，为实测状态方程做好准备；第三章简单介绍了一维三温流体力学数值模拟程序Hyades并运用它进行了若干状态方程实验的计算和设计，进行了烧蚀层厚度对飞片速度、稳定性的影响的定性分析；第四章是实验平台描述部分，介绍了光束平滑化技术，靶的制作，条纹相机的原理和使用，系统同步控制以及光学记录速度干涉仪系统的简单原理和构成。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

The new singular element at the end of a blunt crack is obtained,the new method for calculating stress intensity factors of blunt crack problems is presented.

利用其局部解构造了一种新的大曲率缺口位移模式；建立含大曲率缺口损伤结构有限元方程和与相应的缺口奇异单元；提出了求解大曲率缺口应力与应力强度因子等断裂参量的数值计算方法，数值算例说明本文方法是一种有效的数值计算分析方法。

Numerical calculations were accomplished by the directly numerical method of the singular integral equations and a large amount of statistical results were obtained. So the issue of influence was systematically solved.

最后利用奇异积分方程的数值解法进行了数值计算，得到了大量的数值结果，从而系统地解决了一般倾斜裂纹对界面的影响分析。

We take the nonlinear Klein-Gordonequation in an infinite strap and in a cylinder as examples to illustrate how to deal withnonlinear problems by using Jacobi pseudospectral methods.

Jacobi谱方法和拟谱方法数值分析理论的研究极大地丰富了现有谱方法的理论基础，同时将发展泛函分析、数值逼近论和偏微分方程数值解的相关理论。

According to the different dynamic models, the time precise Baumgarte modify technique and the method to solve state equations were used to simulation the flexible impact system, the satisfactional results were obtained.To the control problem.

对于数值模拟问题，针对不同的动力学模型，分别利用精细Baumgarte违约修正法及状态方程的精细积分法对系统进行了数值模拟，得到了满意的数值解。

A detailed model of non-linear parametric excitation vibration coupling the stay cable and the girder, in which the static sag as well as the geometric non-linearity are considered, is proposed in this paper. Based on several numeric examples investigated by the Galerkin method composed with the integration strategy, several kinds of factors effecting stay cable parameter vibration are studied. Another parameter vibration model by the axial excitation is presented and the corresponding nonlinear equations are derived. The smallest excitation amplitude,the transient state and steady state resonance amplitudes, and the changing characteristics of the axial force are obtained by using harmonic balance method. According to numerical examples calculated by numerical integration method, the effects of the inner damping of the stay cables are investigated.

本文创新地提出了斜拉桥拉索-桥面耦合参数振动模型，推导了索-桥耦合非线性参数振动方程组，联合Galerkin法及数值积分方法，对各种特性的拉索进行了数值求解，得出了影响拉索参数振动的各种因素；提出了斜拉索受轴向端激励参数振动模型，导出了模型的非线性振动方程，使用谐波平衡法得出了产生参数振动需要的最小激励幅值、共振时瞬态及稳态的振动幅值及索拉力的变化特性，并用数值积分方法对实际斜拉桥拉索进行了计算，分析了拉索阻尼对参数振动的影响。

The polynomially fitted values of the molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were calculated and tabulated at an interval of 5 K.

通过热容多项式方程的数值积分，得到了这个化合物的舒平热容值和相对于298.15 K的各种热力学函数值，并且将每隔5 K的热力学函数值列成了表格。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。