扩散

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

The relations of electrophoresis velocity, electroosmosis velocity and electric dispersion velocity are also investigated with these expressions. The results show that this new model offers a better explanation for peak compression effect on the migration behaviour of charged solute in CEC. The retention time will be shorter by peak compression effect, which is similar to a solvent gradients process. The peak compression effect is not steady, and doesn't appear until the conditions are fitted in some special situation.

基于弛豫理论所建立的基本模型，在考虑溶质在两相中皆有可能发生正、反向迁移的情况下，得到了流出曲线一阶原点矩和二阶中心矩的理论表达式，并通过对溶质在两相中电扩散速率与电泳速率、电渗流速率关系的分析结果证实：溶质在固定相表面的电扩散行为可以使其保留变弱，出峰加快；而这种电扩散导致的超常柱效峰的出现具有不稳定性，只有在多方面因素综合影响匹配的情况下才可能出现。

Decreasing N diffusion width and distance between N diffusion and emitter of minority carriers current can increase MAAP efficiency.

由模拟结果可知，减小N型扩散区的宽度，减小N型扩散区与少数载流子发射极之间的距离，增加P型扩散区的掺杂浓度以及使第二个衬底接触浮空可以有效地提升多环有源保护结构的效率。

Correlation of the nonlinear kinetic discrete model for diffusion in binary nonuniform system and Fick's laws and Cahn-Hilliard equation is discussed.

研究了二元非均匀体系扩散的非线性动力学离散模型与Fick扩散定律和Cahn-Hilliard扩散方程的相关性。

The chemical wave of the diffusing species propagates much faster than the diffusing species following the Fick's law.

反应物种化学波的扩散速率要远大于遵从Fick定律的扩散物种的扩散速率。

In city , because the occupied area of the urban sewage pumping station is usually limited , the length of the forebay is inclined to be short and the diffusion angle in flow direction is big accordingly , which causes bad flow pattern, such as backflows ,vortices, etc.

城市排污泵站由于条件的限制，前池一般面积较小，扩散角较大，扩散段较短，因此水流进入前池后突然扩散，流态紊乱，易行成回流、漩涡等不良水流流态，从而影响水泵的工作性能。

In Chapter 4, the related mathematical knowledge, methods and principles are presented which include mathematical morphology, Fourier transform and discrete cosine transform, illposed problem and corresponding regularization methods, basic iteration methods and preconditioning technologies.

回顾并比较了传统线性和非线性滤波方法，详细综述了从变分到PDE在图像滤噪与模糊恢复上的应用和发展，模型基本形式为无约束极小化问题：〓（1）惩罚算子L扩散形式为〓（2）Κ为扩散项，是调整扩散程度的关键因子。

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。

The energy-saving and consumption-reducing theory of gas diffusion anode for zinc hydrometallurgy is introduced.

介绍了气体扩散阳极在湿法炼锌上的节能降耗原理，用气体扩散阳极代替普通阳极将降低50%左右的能耗；与此同时，介绍了氢扩散阳极的结构并对它在冶金上的应用进行了展望。

For this reason, the concept "flow point" in the interdiffusion field is proposed and the methods of fluid mechanics are applied to construct the phenomenological theory for describing the interdiffusion growth of solid phase. Two types of phase growth, i.e.

为了解决这一问题，作者借鉴流体力学的基本概念和方法，通过建立固体互扩散区域中"流点"的概念，推导了描述固体互扩散生长的普适方程，严格区别了相的体积生长与界面生长方式，并给出多元扩散偶中相生长的一般动力学描述。

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