查询词典 diffusion equation

It is a generalization of the nonlinear diffusion equation proposed by Perona-Malik and the method presented by Cuesta, and interpolates between the nonlinear parabolic equation and the nonlinear hyperbolic equation, thus can effectively control the diffusion process so that noises can be removed and details of the image such as edges can be preserved as much as possible simultaneously.

提出了一种包含对时间的分数阶导数的非线性扩散方程，它是对Perona-Malik的非线性扩散方程和Cuesta提出的方程的推广，介于非线性抛物方程和非线性双曲方程之间，从而能有效地控制扩散过程，使得在去除图像噪声的同时能够尽可能地保留图像的边缘等细节信息。

Many natural phenomena and physical laws can be described by time dependent nonlinear differential equations, such as heat conduction equation, sound wave and elastic wave equation, reaction diffusion and convection diffusion equation, fluid and aerodynamics equations, etc.

大多数的自然现象与物理规律都可归结为与时间相关的非线性偏微分方程，诸如热传导方程、声波与弹性波方程、反应扩散与对流扩散方程、流体与气体力学方程组等发展方程。

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。

In this paper,a space fractional differential equation is considered.The equation is obtained from the advection-diffusion equation by replacing the second order derivative in space by a fractional derivative in space of order.

考虑空间分数阶微分方程(即在一个标准的扩散-对流方程中，用分数阶导数代替空间二阶导数)，给出了该分数阶微分方程的显式和隐式有限差分格式。

Assuming infinite diffusion medium, based on the diffusion equation for prestressed concrete structure, and accounting for the effects of concrete chloride binding capacity, time dependence of diffusion coefficients, temperature and moisture, models of chloride diffusion in two-dimensional infinite body with both power function and constant homogeneous boundary conditions were formulated.

针对无限大的扩散介质，以综合考虑氯离子结合能力、氯离子扩散系数的时间依赖性和环境温湿度影响的实际预应力混凝土氯离子方程为基础，分别在常数和幂函数边界条件下，推导出二维氯离子扩散理论的齐次模型。

In this paper, a high order accuracy difference method is presented for solving unsteady convection diffusion equation by using Implicit Perturbation Finite Difference scheme. Firstly, we use the steady convection diffusion equation, the constant coefficients of this equation are expanded to power series of grid-spacings, then the high-order Perturbation Finite Difference scheme is obtained by determining the coefficients of the power series. Put this scheme on unsteady convection diffusion equations and modified it, the IPFD scheme is constructed.

本文利用摄动差分思想，对定常对流扩散方程中的空间微商系数进行摄动展开，展开幂级数系数通过消去摄动格式修正微分方程的截断误差项求出，由此获得方程的隐式摄动差分格式，将此方法应用于非定常对流扩散方程，并加以修正，得到该方程的修正隐式摄动差分格式。

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。

One way is to regard them as the random variables submit to a certain distribution; another is to take them as a random process—— we derive random variables form any of its function's time development, and, the diffusion equation could be partially approached by a equation which is similar to the Ito stochastic integral equation so that the Ito stochastic integral equation is inter-related with the diffusion equation. Therefore, this process could basically reflect the uncertainty in different models.

PSFEM法是假定基本随机变量在均值点处产生微小摄动，利用Taylor级数把随机变量表示为确定部分和由摄动引起的随机部分，从而将有限元控制方程转化为一组线性的递推方程，求解得出位移的统计特性，进而求出应力的统计特性。

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。

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。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失