数值方程

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Based on parabolized stability equations , the stability of nonparallel boundary layer is calculated and analyzed by using recursion numerical method.

该文从抛物化稳定性方程出发，采用从上游往下游递推的数值方法，对非平行边界层稳定性问题进行了数值计算和分析。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

The key elements and techniques of the numerical wind tunnel are studied and analyzed.The basic idea of CFD is expatiated and the whole working process is presented.Discrete methods of the control equations based on the finite volume method and the PISO algorithm about the fluid numerical computation are researched also.

对基于CFD的数值风洞关键基础和技术进行研究分析，阐述了CFD的基本思想，研究了基于有限体积法的控制方程的离散方法以及流场的数值求解的PISO算法。

The gas phase Reynold's average Navier-Stokes equation and the Lagrangian method were adopted to simulate the spray of water liquid jet injected into air stream.

采用气相的时均雷诺方程，在拉格朗日框架下求解离散相的运动方程，对水与空气交叉流动的喷雾流场进行了数值模拟研究。

Model, then calculated the tidal consistent constant and saved as map layer as the data for tidal fast prediction. The result of comparing the model result and investigative data indicated its rationality.Later applied the model in the numerical predication of sinkable chemicals spilled beside ZhuHai region.

分析近海水域环境污染扩散数值模拟的研究应用现状基础上，根据沉降型化学品的性质及其在海上的行为特点，分别建立沉降型化学品行为数值模拟的对流扩散方程模式和粒子拉格郎日迁移模式，确定求解方式并将其软件化。

Transport of organic chemicals in soil vadose zone was simulated by using a coupling model of solute transport and water flow.

采用溶质传递方程和水流动方程联立耦合进行数值求解，模拟土壤渗流区中有机污染物的垂直一维迁移过程。

Practical microstrip antenna problems, such as the effect of superstrate on input impedance and radiation pattern are studied.

根据所得的新公式建立了多层介质覆盖矩形贴片微带天线的积分方程，并利用有效的数值技术求解出上述方程，得到了贴片上的电流分布，进而求出天线输入阻抗和辐射方向图。

At the same time, variational equations, their finite element formulations and numerical convolved integration algorithm of the model in current configuration usually called co-moving coordinate system are given.

基于非线性几何场论，建立了材料非局部连续模型、变分方程及相应的实时拖带系大变形有限元数值模型，设计了这一模型的数值卷积算法。

In the second part of of this thesis, we firstly derivate the operation condition of intracavity SHG of dualwavelength laser from the rate equation, and then numerically calculate the relationship between the laser operation parpmeters and the pumping powers. And then we discuss two possible ways to get balancing outputs of the harmonic waves of the two wavelengths. By comparing the two ways, we find that the method by increasing the geometrical factor of 1079. 5nm SHG has the higher efficiency than the method by adding the additional loss of 1079. 5nm basic wave. Besides, the first method is easier to realize in experiment than the second method.

本论文第二部分从速率方程出发，通过求解速率方程的稳态解得到了Nd：YAP腔内倍频双波长激光的连续运转条件，数值计算得到了随泵浦功率变化的激光运转情况；计算、分析了通过增加主波长的倍频耦合几何因子和增加主波长的腔内损耗两种方法获得均衡的双波长倍频输出的运转情况，通过二者的比较，发现增加倍频耦合几何因子的方法比增加损耗的方法效率更高，而且在实验上更易于实现。

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。