查询词典 interior boundary problem

LBIE, based on the local boundary equation, adopts the traditional moving least squares approximation which depends on only the values of the nodes in the domain of the problem or along its boundary. The whole process of integration is carried on over a local domain or its local boundary centered at the node in question. The local boundary equation can be rewritten to represent the values of the unknown function at the point of interest, and the essential boundary conditions can be directly and easily enforced by using the Green formula and the characters of the Dirac function.

它以局部边界积分方程为基础，采用移动最小二乘近似函数，从而只需要分布在问题域内及其边界上的节点的信息值，无需划分单元；整个积分是在以节点为中心的局部域及其边界上实现，所以不需要背景积分网格；借助于格林公式及Dirac函数的性质，将局部边界积分方程转化为所考虑点的未知函数的边界积分表达式，便于直接施加本质边界条件。

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

Coordinate sequence method is made up of the instruct information of polygon boundary x, y coordinate. It is the easiest polygon vector encoding method. The file structure of this method is easy, but because of the polygon boundary has stored two times, it will produce data redundancy, moreover, short of neighbor threshold information; Tree index encoding method make all the boundary points digitizing, store the coordinate sequence, connect the point index to boundary line, and then connect the line index to other polygons, so as to the tree index structure has came into being. It eliminates neighbor polygons boundary data redundancy problems; Topology structure encoding method is a method which by setting up a complete topology relationship structure, resolve the neighbor threshold and island information process problem. However, it makes arithmetic more complicated and makes database bigger.

坐标序列法是由多边形边界的x，y坐标对集合及说明信息组成，是最简单的一种多边形矢量编码法，文件结构简单，但多边形边界被存储两次产生数据冗余，而且缺少邻域信息；树状索引编码法是将所有边界点进行数字化，顺序存储坐标对，由点索引与边界线号相联系，以线索引与各多边形相联系，形成树状索引结构，消除了相邻多边形边界数据冗余问题；拓扑结构编码法是通过建立一个完整的拓扑关系结构，彻底解决邻域和岛状信息处理问题的方法，但增加了算法的复杂性和数据库的大小。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

The main aim of this thesis is to study some boundary value problems for complex Monge-Ampere equations ,which contain the semilinear oblique boundary problem,infinite boundary value problem and Dirichlet boundary problem in some special domain that is not strictly pseudoconvex.

近20年来，对于复Monge-Ampere方程的研究已经取得了丰硕的成果。

A novel hybrid algorithm, which combines predictor-corrector primal-dual interior point method and genetic algorithm, is presented for dynamic and static reactive optimization in this dissertation. The algorithm fully make use of the advantage of interior point method in solving successive optimization problem and the advantage of genetic algorithm in solving discrete optimization problem. The original problem is divided into three parts: total successive problem, discrete problem and successive problem.

结合内点法和遗传算法，本文提出了一种新颖的混合算法用于求解动、静态无功优化问题，算法充分利用了内点法易于求解连续优化问题和遗传算法易于求解离散优化问题的优势，将原优化问题分解为初步的连续优化问题、离散变量优化问题、连续变量优化问题这三个子问题分别求解。

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。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

According to the different orientations of domain walls with respect to the (100) observation plane of a foil, 90°domain boundaries may be divided into two kinds. one is thin lens or ring shaped a-a 90°domain boundary, and the domain wall lies on the {110} plane; Usually, most of these domain boundaries are uncharged; according to the extinction rules for the (011) domain walls, the displacement vector 〓 along 〓 can be dertermined, which is parallel to the line of intersection between the domain wall and the plane consisting of spontaneous polarization vectors on both sides of domain boundary; from selected area electon diffraction of crystals including domain boundary, we not only examine slight difference in the crystal parts on both sides of the domain boundary, but also obtain crystallographic relationship between them, that is, there exists a 180°rotation symmetry operator along a normal of domain wall. The other is Z or ring shaped a-c 90°domain boundary along {010} direction, and the displacement vector 〓 runs along 〓 direction.

根据界面相对于样品中(100)观测面取向的不同，90°畴可分为两类：一类为薄透镜片状或环状的a-a90°畴，其界面平行于{110}，多数不带电，由消光规律可确定其位移矢量平行于畴界面与自发极化所在平面的交迹，即，〓方向，而从包含畴界的选区电子衍射图可知，这种不带电的90°畴界两侧存在微小的取向差，其界面两侧的结晶学关系为以界面法线为二次轴的旋转关系；另一类为Z状或环状的a-c90°畴，其界面平行于[010]或[001]，相应的位移矢量为〓方向。

The main creating aspects are finding and clarify such a fundamental physical process that the grain boundaries emit vacancies under compressive stress to induce solute non-equilibrium grain boundary dilution and absorb vacancies under tensile stress to induce non-equilibrium grain boundary segregation, formulizing the structural equations and the composition equations in force equilibrium in grain bounary region to describe this physical processes and the kinetic equations for non-equilibrium grain boundary segregation under tensile stress, calculating the modulus in grain boundary region from the expermental data of grain bounday segregation using the structure and coposition equations and calculating the diffusion coefficients of vacancy-solute atom complexes using the kinetic equation simulating the experimental results of grain boundary segregation.

本项目的主要创新点是，发现并阐明了弹性应力场作用下空位与晶界交互作用的基本物理过程：在张应力作用下，晶界会吸收空位，引起溶质非平衡晶界偏聚；压应力作用下，晶界会发射空位，引起非平衡晶界贫化。建立了描述此物理过程的晶界区力学平衡的结构方程和成分方程；？建立了张应力引起的非平衡晶界偏聚动力学方程？；用晶界区力学平衡的结构方程和成分方程？，首次通过实验测量计算出多晶材料晶界区的弹性模量；通过建立的动力学方程模拟实验结果，首次获得溶质原子－空位形成的复合体的扩散系数。

Molecular Distillation is a kind of high vacuum distillation method, which is suitable for the separation of high boiling, heat sensitivity and viscidity products.

分子蒸馏技术是一种在高真空条件下进行的连续蒸馏过程，适合于分离高沸点、热敏性及具有生物活性的混合物。

They are to the Noughties what yuppies were to the Eighties .

那在六十年代是时髦的，但在八十年代肯定是过时了