轴对称金属模具电磁热裂纹止裂中热应力场的分析

为求解金属模具脉冲放电止裂瞬间裂纹尖端附近的热应力场,选择具有半埋藏环形裂纹的金属凹模为研究对象,采用复变函数方法求解了凹模内外环面均匀通入强脉冲电流放电止裂时的热应力场．理论分析结果证实:由于放电瞬间脉冲电流的绕流集中效应,使金属凹模内部环形裂纹尖端附近金属迅速升温,金属熔化形成堆焊,并由于瞬间温升产生热压应力场．研究结果表明:应用电磁热效应止裂技术可以减小裂纹尖端的应力集中,形成的热压应力场有效地阻止金属模具中干线裂纹源的开裂趋势,达到了裂纹止裂目的．     

带合作行为的平均场模型的依全变差稳定性

该文考虑一个带合作行为的平均场模型的稳定性问题. 应用耦合方法, 建立了相应于这个平均场模型的扩散过程的依全变差稳定性.     

轻质热防护系统多层材料组合结构的热应力分析

提出了轻质热防护系统外面板使用多层结构的概念,设计了2种热防护材料组合构成的3种铺层方案．通过模拟飞行器再入大气层时受到的机械和热载荷条件,数值计算得到了层间剪切力、底部温度和y方向位移．计算结果发现,层间剪切力发生在边缘部位且呈反对称分布;选用高热导率和高热容材料能够减少材料内的温度梯度,进而有效地降低结构的热应力和热变形;在均匀温度场情况下,两种材料的热膨胀系数之差越小,则层间剪切力越小．该研究表明不同的材料组合和铺层次序的多层结构,可以满足不同设计要求,具有优化设计潜力．     

三维浮式结构的流固耦合动力特性分析

对于采用位移-压力有限元格式从流固耦合系统导出的大型非对称矩阵特征值问题,构造出了一种新格式的迭代Arnoldi方法进行非对称特征值分析来获得浮式结构的动力特性．该迭代格式在克服零频的移频技术中,可以高效地计算出Arnoldi向量．实例分析结果表明,流固耦合作用对水上大型薄壁浮式结构动力特性具有重要影响．     

对基频光与低强高频光形成的双色场的计算与分析

基频光及一弱的辅助高倍频光（9倍 、1３倍甚至120倍频光等）的双色场（该场高频光强度仅为基频光的1/100）作用于氦离子He⁺,发现高次谐波辐射的效率有了很大的提高,尤其是相应于入射高频光频率对应级次及邻近级次的谐波效率有极大提高. 加入不同的低强高频光对双色场高次谐波产生的影响进行计算及讨论,并对其物理机制进行初步阐释.     

具有二阶逼近效应场多维Landau-Lifshitz 方程解的极限行为

本文给出在Rⁿ⁺¹ 到S² 整体光滑映射控制下的极大值原理, 通过这个原理建立具有二阶逼近效应场多维Landau-Lifshitz 方程的δ- 黏性上解和δ- 黏性下解. 利用这些δ- 黏性上下解, 我们建立具有二阶逼近效应场多维Landau-Lifshitz 方程的黏性解并获得解的极限行为, 即存在两个不相交的开子集M 和N 使得δ- 黏性上解和δ- 黏性下解分别在M 内任一紧子集上趋于(0, 1, 0), 在N 内任一紧子集上趋于(0,?1, 0).     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

预倒出口箱区的多场桥调度优化

在集装箱出口箱区堆场的实际作业中,常将待提箱提前翻倒至一空闲箱区,使其装船前以船舶配载图的倒序堆垛,以提高装船效率。为提高初始出口箱区的预翻作业效率,针对该箱区的多场桥调度优化问题进行研究。以实施预翻作业的某一出口箱区为研究对象,在船舶配载图已知的前提下,考虑作业场桥间保持安全距离且不可跨越的条件,兼顾满足经验翻箱规则等现实约束,侧重作业过程中实时翻箱,构建了以场桥作业总行走时间最小为优化目标的线性规划模型,并设计了分支定价算法。在算例实验中,通过与非实时预翻箱方案、FCFS方案以及下界进行对比,验证了模型及算法的有效性,可为集装箱码头出口箱堆场的场桥调度提供参考。     

接触表面中多场耦合方程的边界层特征解

介绍由约束场和受重力影响的对流扰动耦合而成的衰减平衡向量场动力学方程的渐近求解.为分析实验室内微观与自然界中宏观现象的正则和奇异扰动问题.运用复合尺度方法进行Fourier调和分析、尺度变化,并引进新的参数,将一个复杂的三维约束耦合动力学方程降维投影并转化成复空间里一维的边界层问题.通过渐近摄动分析,给出多场耦合中扰动问题的特征函数边界层解法,在例2中对流场扰动问题分析,得出从指数振荡解过渡到代数解的转点.进一步分析计算非线性特征值问题并做了渐近摄动分析,最后给出多场耦合中扰动问题的特征值边界层解法.最后,特征关系式的各参数表明其在接触表面中对动力衰变的关键影响.     

多分量的KN族与可积耦合及其它们的哈密顿结构

Firstly,a vector loop algebra (~G)3 is constructed,by use of it multi-component KN hierarchy is obtained.Further,by taking advantage of the extending vector loop algebras (~G)6 and (~G)9 of (~G)3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively.Finally,Hamiltonian structures of obtained system are given by quadratic-form identity.     

Multimaterial Lattice Structures With Thermally Programmable Mechanical Behaviors北大核心CSCD

传统的点阵结构一旦制备完成,其力学性能通常在使用寿命内保持不变。设计和制造具有环境适应特性的智能点阵结构,可编程地感知和响应外界变化(例如光强、压强、溶液、温度、电磁场、电化学激励),并在时间和空间上进行形状重构、模式转换和性能调控,仍然是人造材料研究领域重要的科学挑战。该文采用具有不同玻璃化转变温度和温度依赖性的多种聚合物材料,通过合理设计材料空间分布,提出了一类具有热可编程力学响应能力的多材料点阵结构。结合理论分析和有限元模拟,研究了组分材料相对刚度对多材料点阵结构的Poisson比、变形模式以及结构稳定性的影响。通过温度变化实现了对多材料点阵结构弹性常数、压溃响应和结构稳定性的调控,使多材料点阵结构表现出极大的热变形、超弹性和形状记忆效应。为设计和制造自适应保护装备、生物医学设备、航空航天领域的变形结构、柔性电子设备、自组装结构和可变形软体机器人等开辟了新途径。     

Definability of Geometric Properties in Algebraically Closed Fields

We prove that there exists no sentence F of the language of rings with an extra binary predicat I₂ satisfying the following property: for every definable set X ? ?², X is connected if and only if (?, X) ? F, where I₂ is interpreted by X. We conjecture that the same result holds for closed subset of ?². We prove some results motivated by this conjecture.     

Explicit Geometric Integration of Polynomial Vector Fields

We present a unified framework in which to study splitting methods for polynomial vector fields in R ⁿ . The vector field is to be represented as a sum of shears, each of which can be integrated exactly, and each of which is a function of k<n variables. Each shear must also inherit the structure of the original vector field: we consider Hamiltonian, Poisson, and volume-preserving cases. Each case then leads to the problem of finding an optimal distribution of points on an appropriate homogeneous space, generally the Grassmannians of k-planes or (in the Hamiltonian case) isotropic k-planes in R ⁿ . These optimization problems have the same structure as those of constructing optimal experimental designs in statistics.     

凸函数的几何特征与分类

由凸函数的充要条件,证明关于凸函数的三个命题,据以讨论凸函数的几何特征,给出凸函数的三种分类以及其对应图形,由此得出关于凸函数的几个结论.     

Artin空间中SU(3)规范场的几何解析

研究4维Artin空间中SU(3)规范场的线性化问题.首先对Yang-Mills方程的推导进行了讨论,给出了恰当的Yang-Mills方程的概念,其具有明确的几何意义.其次,构造了一类线性微分变换,称之为Artin空间SU(3)规范场的示性变换.示性变换是应用数学机械化方法确定的.经由示性变换,将非线性的恰当的Yang-Mills方程变为一组线性方程,实现了SU(3)规范场的场方程的线性化.从而证明了,对于恰当的Yang-Mills方程,SU(3)规范场包括8个独立的规范场.     

A Global Geometric Decomposition of Vector Fields and Applications to Topological Conjugacy

We give a global geometric decomposition of continuously differentiable vector fields on \(\mathbb{R}^{n}\). More precisely, given a vector field of class \(\mathcal{C}^{1}\) on \(\mathbb{R}^{n}\), and a geometric structure on \(\mathbb{R}^{n}\), we provide a unique global decomposition of the vector field as the sum of a left (right) gradient-like vector field (naturally associated to the geometric structure) with potential function vanishing at the origin, and a vector field which is left (right) orthogonal to the Euler vector field, with respect to the geometric structure. As application, we provide a criterion to decide topological conjugacy of complete vector fields of class \(\mathcal{C} ^{1}\) on \(\mathbb{R}^{n}\) based on topological conjugacy of the corresponding parts given by the associated geometric decompositions.

     

具有迷向S曲率Randers度量的几何意义

Riemann流形上的Zermelo航行为Randers度量提供了一个简洁而且清晰的几何背景．在这个背景下D．Bao，C．Robles和Z．Shen对于具有常旗曲率的Randers度量进行了完全分类．这篇论文中，我得到了判定具有特殊曲率性质的Randers度量的两个充分必要条件．从这两个条件出发，我得到了迷向S曲率的Randers度量的几何意义和一系列推论，并且构造了具有迷向S曲率Randers度量的新例子．最后，在Zermelo航行的背景下研究了Berwald型的Raiders度量．     

Model Based Estimation of Geometric Characteristics of Open Foams

Open cell foams are a class of modern materials which is interesting for a wide variety of applications and which is not accessible to classical materialography based on 2d images. 3d imaging by micro computed tomography is a practicable alternative. Analysis of the resulting volume images is either based on a simple binarisation of the image or on so-called cell reconstruction by image processing. The first approach allows to estimate mean characteristics like the mean cell volume using the typical cell of a random spatial tessellation as model for the cell shape. The cell reconstruction allows estimation of empirical distributions of cell characteristics. This paper summarises the theoretical background for the first method, in particular estimation of the intrinsic volumes and their densities from discretized data and models for random spatial tessellations. The accuracy of the estimation method is assessed using the dilated edge systems of simulated random spatial tessellations.     

Continued Fractions of Functions Connected With Real Quadratic Function Fields

The theory of continued fractions is very useful in studying real quadratic number fields(see [2-5]). E. Artin in [1] introduced continued fractions of functions to study quadratic function fields, using formal Laurent expansions, which is essentially the theory of completion ofthe function fields at the infinite valuation. Here we first re-develop the theory of continuedfractions of functions in a more elementary and manipulable manner mainly using long divisionof polynomials; and then study …     

Experimental Investigation into the Mechanical Behavior of Textile Composites with Various Fiber Reinforcement Architectures

Mechanics of Composite Materials - The role of fiber reinforcement architecture in adjusting the mechanical properties of glass-fiber-reinforced epoxy composite materials is studied. Fibrous...