查询词典 diffusion equation

A quasi one-dimensional, time dependent system model based on the parallel compressor theory was used to compute the effect of inlet distortion on turbine engine stability; Through Modifying steady state continuum equation, momentum equation and energy equation, the effect of power extraction and additional bleed on turbine engine running line was computed. Unsteady state continuum equation, momentum equation and energy equation were solved for computing the effect of acceleration on turbine engine running line.

其中，进气畸变对发动机气动稳定性影响的计算采用平行压气机模型，基于李亚普诺夫理论的方法完成；附加引气、功率提取对发动机气动稳定性的影响采用通过对发动机转子间质量、动量、能量守恒方程进行修正的方法进行；加速过程对发动机气动稳定性的影响采用欧拉方法求解动态的质量、动量、能量守恒方程的方法完成；最后采用&层迭&的方法进行各种降稳因素的综合评估。

Based on the point that directed diffusion equation is a diffusion process with direction, the correlation between directed diffusion and wavelet transform is studied in this paper.

摘要方向扩散方程是一种有方向性的扩散，本文基于这一特点，对方向扩散方程与小波分解和重构的相关性作了研究。

The combustion events in the swirl chamber and the main chamber are processed differently. The combustion in the swirl chamber is broken into three phases: low temperature ignition, high temperature premixed combustion and flamelet diffusion combustion, while the combustion in the main chamber is only considered as flamelet diffusion combustion. The Shell ignition model, global Arrhenius equation and coherent flamelet model are used to describe low temperature ignition kinetics, high temperature premixed kinetics combustion and flamelet diffusion combustion respectively.

把涡流室式柴油机不同区域与不同时期的燃烧过程分开处理，将涡流室中的燃烧过程划分为三个性质不同但相互重叠的阶段：用Shell着火模型模拟的低温着火化学动力学反应阶段，用Arrhenius方程模拟的高温预混燃烧化学动力学反应阶段和用相关火焰微元模型模拟的扩散燃烧阶段，认为主燃烧室的燃烧只有相关火焰微元的扩散燃烧阶段。

Based on this equation, the effect of pressure, temperature on liquid diffusion coefficients was dis〓sed, then the mutual diffusion coefficients at infinite dilution of 35 binary systems and self-diffusion coefficients of 12 pure substances under high pressure have been calculated.

根据该方程讨论了温度、压力对液体扩散系数的影响，并计算了高压下35个二元物系的无限稀释扩散系数与12个纯物质的自扩散系数。

In the first part, it was investigated the interaction between Pb2+ and La4Ti9O24 ceramic bulk. The result shows that a significant Pb2+ diffusion into La4Ti9O24 ceramic bulk and a significant crystallization of the La2/3TiO3-type phase is clearly observed in the Pb2+ diffusion layer. The reacted zone consists of the La2/3TiO3-type phase exhibits the linear dependence of the square of the thickness, x, on the heat-treated time, t, in excellent agreement with the parabolic law x2 = kt, where k is the growth rate coefficient. The kinetic study thus indicates that the Pb2+/La4Ti9O24 interaction strictly obeys the theory of the reactive diffusion. Furthermore, the experimental k values were used to determine the associated activation energy, Ea, for the formation of La2/3TiO3-type phase using the Arrhenius plot and the following least-square equation, ln =-Ea/RT + A, where T is the annealing temperature, R is the universal gas constant, and A is a constant, resulting in Ea ~ 607 ?b 60 kJ/mol.

首先， 以巨观的方式观察PbO与La4Ti9O24陶瓷体介面的反应现象；利用X-ray绕射分析以及扫描式电子显微镜来观察不同的热处理温度以及不同的持温时间所制作的样品，研究结果发现， Pb2+离子会渗入到La4Ti9O24陶瓷内，同时在Pb2+离子所渗入的区域内会产生新的La2/3TiO3-type钙钛矿斜方晶相；藉由量测不同温度与时间之样品，其因Pb2+离子渗入而产生之La2/3TiO3-type相层厚度之关系，符合反应式扩散机制中 x2 = kt 之关系式(其中 x：扩散层厚度； k：反应速率常数； t：反应时间)；进一步将不同实验条件所得到之反应速率常数值代入Arrhenius方程式ln (k =-Ea/RT + A ，其中Ea：活化能； T：绝对温度； R：气体反应常数； A：常数，可以求得Pb2+离子与La4Ti9O24陶瓷发生反应式扩散所需之活化能为607 ± 60 kJ/mol。

By using the Eulerian-Lagrangian combined method, the convection-diffusion equation is spitted into the diffusion terms and convection terms. For convection terms, the implicit method of characteristics using time-line interpolation with high accuracy is adopted. While for the diffusion terms the conventional finite difference method is used.

采用欧拉—拉格朗日混合解法，将对流—扩散方程中的扩散项和对流项分裂求解，应用高精度时间序列插值的特征差分隐格式求解对流项，扩散项采用传统的有限差分法。

Any high Re number flow over bodies consists of three basic flows: the flow with convection-dominant in all spatial directions, the flow with convection-diffusion competition in all directions and the flow with convection-dominant in part directions and convection-diffusion competition in part directions, which is called the interacting shear flow; the features of the three basic flows are different; their simplest conservation equations, i.e. the Euler equations, Navier-Stokes equations and diffusion parabolized NS equations, have different mathematical characteristics; there is a great disparity in domains of the three basic flows and the domains of NS equations are very small. Therefore, adopting Euler-DPNS-NS equation system to analyze and compute high Re number flows over bodies is a logical approach. There exists a mutual examined-complemented relationship of this approach with the usual one of adopting only NS equations.

主要内容如下：（1）高Re数绕流包含3种基本流动：所有方向对流占优流动、所有方向对流扩散竞争流动和部分方向对流占优部分方向对流扩散竞争流动，3个基本流动的特征彼此不同且在流场中所占领域大小彼此相差悬殊，NS方程区域很小，它们的最简单控制方程组Euler、Navier-Stokes和扩散抛物化NS方程组的数学性质彼此不同，因此利用Euler-DPNS-NS方程组体系分析计算高Re数绕流流动就是一个合乎逻辑的选择，该法与利用单一NS方程组的常用方法可以彼此检验和补充。

Secondly, this paper set up the diffusion model of innovation incorporating price, advertising and distribution, and given the optimal diffusion equation and characterized qualitatively optimum price, advertising and distribution. Furthermore, it studied the ratio relations among the advertising elasticity of demand and the price elasticity of demand and the distribution elasticity of demand. Finally studied the influence of marketing mix variables to the technology diffusion.

然后建立了含商品定价、广告费用和销售费用等的技术创新扩散模型，给出了扩散最优方程和商品价格、广告费用和销售费用的最优曲线，进一步地，本文分析了广告费用对需求的弹性、商品定价对需求的弹性以及销售费用对需求的弹性之间的比例关系，探讨了这些外部市场变量对创新扩散的影响。

For intramolecular electron transfer reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.

对于扩散控制的溶液中的电子转移反应，分子内振动模的运动比溶剂运动快很多，Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动，而分子内的振动用sink函数来表示，我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程，并将其应用于嗪1(oxazine 1，OX1)和N，N-二甲基苯胺分子之间的电子转移反应，Sink函数采用几种不同的微扰表达式，通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数，揭示了该体系电子转移过程中的一些动力学性质。

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

In the chapter 2, the theoretic knowledge about the photosensitive resin and the grinding tools was firstly introduced.

第二章阐述了光固化树脂结合剂磨具的相关理论研究。

Do not use the program's indenting or margin-setting features; these will be added during typesetting.

不要使用缩排，页面边缘设置之类的选项，偶看不大懂。