复合材料反平面切口端部奇性研究

基于复合材料切口尖端位移场的渐近展开,将切口的反平面平衡控制方程转化为关于切口奇性指数的特征微分方程,采用一种变换将其化为线性特征微分方程组,引入插值矩阵法计算相应边界条件下方程组的特征值以获取切口尖端的应力奇性指数.研究单相材料切口、双相材料切口及止于异质界面切口的奇异性,算例表明该方法可以一次性计算出多阶奇性指数.对所取得的非奇异指数尽管切口不表现出奇性状态,但却是描述切口尖端完整应力场必不可少的参量.     

双压电材料三维界面端部力电耦合场奇异性

基于切口根部物理场的幂级数渐近展开假设,从三维应力平衡方程和麦克斯韦方程组出发,导出关于双压电材料楔形界面切口端部奇性指数的特征微分方程组,并将切口的力电学边界条件表达为奇性指数和特征角函数的组合,从而将双压电材料楔形界面切口端部奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解,运用插值矩阵法求解界面端部若干阶应力奇性指数和相应特征函数.计算结果与已有结果对比表明本文方法的有效性和具有较高的计算精度.     

边界元法分析二维线弹性裂纹扩展

用边界元法研究裂纹扩展过程.首先将尖端区域Williams渐近展开的特征分析法与边界积分方程结合,解出切口尖端附近应力奇异性区域的各应力场渐近展开项系数,获得平面切口/裂纹结构完整的位移和应力场.再基于考虑非奇异应力项贡献的最大周向应力脆性断裂准则,运用边界元法分析边缘含裂纹半圆形弯曲试样在荷载作用下的启裂方向,对裂纹扩展过程给出自动跟踪方法,通过算例证明边界元法模拟裂纹扩展过程的正确性和有效性.     

熔石英表面热致应力对激光损伤行为影响的研究

为了研究热致应力对光学元件损伤特性的影响,通过实验测试退火处理消除热应力和未消热应力石英基片的激光损伤特性,研究了热致应力对石英元件初始损伤阈值、损伤增长阈值以及损伤增长规律的影响.结果表明,热致应力对熔石英光学元件的初始损伤阈值有影响,初始损伤阈值随着热致应力增大而降低;热致应力会加剧激光引发的损伤增长,相同的激光通量下,表面应力越大的区域拥有越高的损伤增长因子,但损伤增长仍遵从指数增长规律.热致应力对损伤增长阈值没有明显的影响.本文的研究将为CO2激光预处理工艺能否被应用于大口径光学元件提供一个必要的技术参考.     

电子-正电子散射与电子-电子散射的极化效应

计算了电子-正电子散射的16种极化散射截面.根据角分布的特征,它们可以分为三大类,其前向奇性分别是sin~(-4)(θ/2)、sin~(-2)(θ/2)和1.也计算了电子-电子散射的16种极化散射截面,它们既可以按前向奇性分为三大类,也可以按后向奇性分为三大类.三类奇性的特征与电子-正电子散射类似.对于三类奇性的出现给出了直观的物理说明.     

纯物质自由枝晶生长特征的Fourier变换研究

本文用光学中Fourier变换的概念和方法处理纯物质自由枝晶尖端前沿的热势波传输问题,进而描述其凝固界面生长形态变化特征。具体做法是:先将热势波与枝晶端部作用后的传播过程用Fourier变换表示出来,从而求得了热势的空间分布,再由热势的分布特征反推出枝晶尖端界面生长形态的演化特点。这种方法还可简洁地处理界面能各向异性对界面凝固生长特征的作用问题。     

运用改进的无单元Galerkin方法分析机场道面断裂力学问题

在改进的无单元Galerkin方法的基础上,将能反映裂纹尖端附近应力奇异性的特征项r~(1/2)引入改进的移动最小二乘法的基函数中,将断裂力学和改进的无单元Galerkin方法结合,研究了线弹性断裂力学的改进的无单元Galerkin方法,并对含反射裂缝的机场复合道面层状体系结构进行了数值分析.本文的理论为机场复合道面断裂力学分析提供了一种新方法.     

基于准连续介质方法模拟纳米多晶体Ni中裂纹的扩展

通过准连续介质方法模拟了纳米多晶体Ni中裂纹的扩展过程.模拟结果显示:裂纹尖端的应力场可以导致晶界分解、层错和变形孪晶的形成等塑性形变,在距离裂纹尖端越远的位置,变形孪晶越少,在裂纹尖端附近相同距离处,层错要远多于变形孪晶.这反映了局部应力的变化以及广义平面层错能对变形孪晶的影响.计算了裂纹尖端附近区域原子级局部静水应力的分布.计算结果表明:裂纹前端晶界处容易产生细微空洞,这些空洞附近为张应力集中区,并可能促使裂纹沿着晶界扩展.模拟结果定性地反映了纳米多晶体Ni中的裂纹扩展过程,并与相关实验结果符合得很好     

体心立方金属钽Ⅱ型裂纹尖端缺陷萌生的多尺度分析

本文采用多尺度准连续介质法(quasi-continuum method, QC)模拟体心立方(body-centered-cubic, bcc)金属钽(Ta)Ⅱ型裂纹尖端位错的形核与发射过程,获得位错发射位置与应力强度因子关系曲线,分析裂纹尖端缺陷萌生过程,研究全位错分解以及扩展位错形成机理. 位错活动在不同阶段表现出不一致的特征,新位错的发射对于位错运动具有促进作用. 研究表明,裂纹扩展初始阶段首先萌生点缺陷,点缺陷随着加载强度增加会萌生新的点缺陷,点缺陷最终运动到边界,导致Ⅱ型断裂破坏. 在全位错发射之前有不全位错的形核与发射表明全位错的分解分步进行,从势能曲线上来看,也就是两个极小值点的形成机理不同. 关键词： 多尺度 准连续介质法 Ⅱ型裂纹 扩展位错     

分布式布喇格反射镜的穿透深度计算

采用特征矩阵法分别计算奇、偶数层布喇格反射镜的反射相移,利用反射时延与反射相移的关系给出了其穿透深度的表达式.采用电子束热蒸发的方法制备了结构为[HL]2H的布喇格反射镜,并制作了有机微腔器件,测量和计算了其透射光谱、反射相移和穿透深度,得到了微腔的有效腔长,测量值与实验值吻合较好,验证了该穿透深度公式的正确性.     

Interaction of the near field with a gyrotropic sectorial structure

A matrix method is proposed to obtain the characteristic equations for quantities governing the degree of the field singularity on the edge of sectorial gyrotropic structures. Exact analytic solutions are analyzed for giving mixed boundary conditions on the outer faces of a wedgelike domain.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 64–69, October, 1987.     

Smoothing regularization and particle creation in curved spacetime

A regularization procedure is given for the stress tensor of a quantized field in a background metric. This regularization is shown to be equivalent to a covariant renormalization of constants in the generalized Einstein equations. An example of the massive spinor field in Robertson-Walker universe is considered. Regular values of the stress tensor near the cosmological singularity are found.     

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation (CGR) is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima (WTMM) method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonucleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.     

How quantum is the big bang?

When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.     

磁电弹性体中多条位错与Griffith裂纹

根据本征方程，研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论，得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明：在裂纹的端点及位错点上仍然存在应力的奇异性，离位错点越远处广义力越小，结论与已有的结果相符，证明了结论的正确性.当位错点与裂纹端点距离越近时，裂纹与位错间的应力场越小，并逐渐趋近于零.     

Symplectic model for piezoelectric wedges and its application in analysis of electroelastic singularities

In this paper, a symplectic model, based on the Hamiltonian system, is developed for analyzing singularities near the apex of a multi-dissimilar piezoelectric wedge under antiplane deformation. The derivation is based on a modified Hellinger–Reissner generalized variational principle or a differential equation approach. The study indicates that the order of singularity depends directly on the non-zero eigenvalue of the proposed Hamiltonian operator. Using the coordinate transformation technique and continuity conditions on the interface between two dissimilar materials, the orders of singularity for multi-dissimilar piezoelectric and piezoelectric–elastic composite wedges are determined. Numerical examples are considered to show potential applications and validity of the proposed method. It is found that the order of singularity also depends on the piezoelectric constant, in addition to the geometry and shear modulus.     

On the physical interpretation of the central-symmetric gravitational-field singularities

It is shown that the existence of singularity in the centrally symmetric gravitational field, which is interpreted as a surface with unusual physical properties, follows from equations for the action and the energy of a test particle not using Einstein equations and their solutions. A black hole is treated as a physical model of the singularity in question. The results are compared with the usual interpretation of the singularity in Schwarzschild solutions to Einstein equations.     

一类含时变间隙的强非线性相对转动系统分岔和混沌

建立一类具有时变间隙的两质量相对转动系统的强非线性动力学方程.应用MLP方法求解出变换参数,并运用多尺度法求解该系统发生1/2亚谐共振时的分岔响应方程,采用奇异性理论分析得到系统稳态响应的转迁集,并且得到系统在非自治情形下的分岔特性以及系统的分岔形态.最后通过数值仿真得到系统在间隙和阻尼参数变化下的分岔和混沌行为,发现随着系统参数变化系统将出现周期运动、倍周期运动以及混沌等多种不同的运动形态.