数值方程

Since the presence of a out coupling hole alters the transverse structure of the intra cavity light in a FEL oscillator ,the finite element method is used to the optical field equations and a good proximation is made for the out coupling process in the mirror,and then some numerical results are given.

针对孔耦合波导自由电子激光振荡器腔内光场横向特性，应用有限元法于慢变光场方程，并对输出腔镜上孔耦合过程加以较准确的描述，而后通过对数值结果的分析比较，说明这一模拟方法较好地描述了孔耦合引起的腔内光场横向结构的变化发展特性，改善了模拟结果。

It is proved that Newton iteration method is still quadratically convergent under a weak condition, and a new point is added to Newton s method , i.

本文讨论求解非线性方程的牛顿法，证明牛顿法在一个弱条件下仍保持局部二阶收敛性，给出牛顿法的一点改进，即一个不带导数的单参数的二阶收敛的迭代法，而且分别得到这两种迭代法的收敛因子，最后进行数值实验

A set of quadruply coupled equations (fluid flow, convection-diffusion, energy conservation and mechanical equilibrium) with a number of cross-couplings and coupled constitutive relations is formulated to quantify the multi-physics of oil displacement by CO2 injection, implemented into and solved by using FEMLAB. FEMLAB is the first engineering tool that performs equation-based multi-physics modeling in an interactive environment. With FEMLAB, the coupled multi-physics model can be solved simultaneously. The applicability of this model has been demonstrated through an example of simulations for a two-dimensional reservoir of size 1000 m×1000 m with one injection and one production wells. Model results illustrate the significant importance of the cross-couplings between individual (thermal, hydrological, chemical and mechanical) physics.

首先，建立一套流、固、热、多相流等多场全耦合控制方程组及其相应的耦合本构关系；然后，采用FEMLAB为工具来模拟三次采油阶段CO2驱油过程中的流、固、热、物质守恒等多场之间的全耦合作用，是第一个人机交互式的基于偏微分方程组的多物理场耦合分析的工程工具，利用FEMLAB，该4个耦合方程组成的方程组可以一次同时被求解出来：最后，应用该模型来求解一个二维油田的驱油情况，数值计算结果表明，原位应力、注入温度、注入压力等因素对CO2的地下贮存效率、驱油速度等有重要影响。

Aslak Tveito and Ragnar Winther,Introduction to Partial differential Equations: A Computational Approach,Springer ...

这门课程将将微分方程的理论、数值逼近和相关的应用结合在一起讲述。

It is demonstrated that the frequency drift will break up the phase-locked state of the laser array and induce the spatial instability of the far-field intensity due to phase noise. It is also found that although the evanescent coupling between elementary lasers can restrain these effects to some extent, the restrainability is too limited to be effective when the frequency drift is relatively strong.

通过对耦合激光器阵列动力学方程的数值研究发现，频率漂移将破坏激光器阵列的锁相状态，并引入相位噪声，导致输出远场光强分布不稳定；研究还发现：倏逝波耦合能够对频率漂移的影响起到一定的抑制作用，但这种抑制只在频率漂移较弱时才有效，因此，如果将该阵列用于光束合成，加入相应的抗干扰措施还是很必要的。

To study the feasibility of a new type of sealing fabrication for high pressure, the deformation equation of cylinder-plunyer system at high pressure was derived. Several feature curves were obtained using the numerical solution of Reynold's function.

为探讨一种新型超高压密封结构的可行性，对超高压下钢筒和柱塞的变形量进行了理论推导，通过雷诺方程数值求解，获得了新型密封结构的漏耗特征曲线、液膜压力分布曲线及初始间隙对泄漏量的影响曲线。

Numerical algebra ; matrix ; equation ; symmetric positive semidefinite solution

数值代数；矩阵；方程；对称半正定解

Transmission of Gaussian light pulse in sinusoidally dispersion-compensated system is studied by numerically simulating the solution of non-linear Schroedinger equation.

从含非线性薛定谔方程出发，通过数值模拟，研究了高斯光脉冲在正弦型色散补偿系统的传输，得到结论：当系统的二阶色散的平均值为零时可得到高斯光脉冲的稳定传输。

This method is also available for other problems of unsteady flow around complicated bluff bodies at medium or high Reynolds numbers and the results are used as reference for wake control The phenomena of the sinusoidally oscillating flow past a circular cylinder are also studied.

本文应用有限差分方法求解涡量-流函数形式的N-S方程，数值模拟了园柱瞬时起动后流动分离、旋涡生成、脱落以及随时间推进涡街产生和长期非定常演化过程，包括对称涡的生成，二次涡形成的α结构及卡门涡街等。

The research work is mainly focused on the phase mask method, the characteristics of near-field diffraction of the phase mask are analyzed with scalar diffraction theory, and the properties of grating formation are studied specifically when the writting light beam incidents normally and slantly, respectively, with some important conclusions derived.

我们首先采用按理想波导模展开的方法建立了FBG中的模式耦合方程，并用模式耦合理论研究了FBG中的模式耦合现象，导出了FBG的反射光谱和透射光谱的理论表达式，采用数值模拟计算的方法研究了FBG的结构参数对其反射光谱特性的影响，得出了若干重要结论。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。