广义对称张量相等的条件

讨论了由广义对称算子诱导的两非零广义对称张量相等的充要条件和广义对称张量为零的充要条件．这里不要求形成可合张量ｗ＝ｘ１　ｘ２　…ｘｎ的ｘ１,ｘ２,…,Ｘｎ是线性无关的．     

各种对称性下挠曲电系数的 Kronecker 张量积表示

Kronecker 张量积在描述材料系数的对称性方面具有重要作用. 通过首次构建符合挠曲电系数对称性的正交旋转张量 4 次 Kronecker 幂, 推导了 7 大晶系、32 类晶体点群及各向同性下挠曲电系数的矩阵结构表示, 这些结果包含了独立的挠曲电系数个数及其具体的分量形式. 通过与前人的工作对比, 验证了本文结果的正确性.     

广义对称张量相等的条件

讨论了由广义对称算子的两非零广义的对称张量相等的充要条件和广义对称张量为零的充要条件,这里不要求形成可合张量ｗ＝ｘ１×Ｘ２×Ｘ．．．ＸＸｎｘ的ｘ１,ｘ２,．．．,Ｘｎ是线性无关。     

地应力三维张量场的可视化技术研究

分析和研究地应力弹性二阶张量场的可视化技术。根据对地应力二阶张量的数学分析,得出了地应力场对应于二阶对称张量,导出了二阶对称张量在空间几何学中对应的二次曲面。结果表明,求取对称二阶张量问题可以归结为求取特征值与特征向量问题。解决了同时表示二阶对称张量场空间一点多个分量的难题和沿地应力某一主方向对称张量及二维对称张量的可视化问题。     

独立分量分析在内燃机噪声信号分离中的应用

采用独立分量分析的方法进行了内燃机噪声信号分离的研究．建立了基于FastICA算法的常规内燃机噪声独立分量分析模型,为了减少所需传声器个数,在此基础上应用了时序独立分量分析模型．以某四缸柴油机为研究对象,测量了不同工况下的噪声信号,计算了这些噪声信号的统计峰度,确认其为非高斯信号,满足独立分量分析的基本要求．对测得的柴油机噪声信号进行了时序独立分量分析,将其分解为一系列不同的独立分量．采用小波变换的方法对它们进行分析,得到了各独立分量的时频分布,研究结果表明,这些独立分量对应着不同的内燃机噪声源信号．     

中心对称半导体表面的面极化率张量及体极化率张量分析

对m3m和432晶系中心对称晶体表面处面极化张量及体极化张量行了系统地分析,并且讨论了将临近表面的跃迁层对反射的二次谐波的贡献分离出来的可能性,表面对非线性光信号的这种贡献来源于表面处对称性的破缺.首次对纵模激光场在非线性介质表面导致的极化率张量的分量情况进行了分析.     

材料晶粒择优取向的定量描述及其在地质学上的应用

材料晶粒择优取向可以用取向分布函数来定量描述，其基本原理是进行坐标变换；一些对择优取向敏感的晶体的力学和物理性能，可以根据这种理论建立其分布函数关系的表达式，在材料织构和岩石组构分析中具有重要意义。文中以立方晶体试样为例，导出了三个取向分量的表达式，描述了试样横向在晶体坐标中的取向。     

材料晶粒择优取向的定量描述及其在地质学上的应用

材料昌粒择优取向可以用取向分布函数来定量描述，其基本原理是进行坐标变换，一些对择优取向敏感的晶体的力学和物理性能，可以根据这种理论建立其分布函数关系的表达式，在材料织构和岩石组构分析中具有重要意义，文中以立方晶体试样为例，导出了三个取向分量的表达式，描述了试样横向在晶体标中的取向。     

SIM(2)引力规范理论

基于宇宙微波背景辐射(Cosmic Microwave Background Radiation,CMB)的各向异性观测结果和马赫原理,假设了洛伦兹(Lorentz)对称性从大于星系尺度开始破缺,并基于这个动机以SIM(2)规范理论为例,诠释了所谓的"暗物质效应",意即天文观测上对牛顿-爱因斯坦(Newton-Einstein)引力理论预言的偏离,可以由小尺度上Lorentz对称性的破缺在大尺度上的累积呈展出来.分析了SIM(2)规范理论,在场运动方程之外得到了8个约束方程,并且将独立contorsion分量个数也约化到了8个.得到了contorsion是非平庸的,并且即使在没有物质分布的区域也会贡献一个等效的能一动张量分布.最后,分析了在弱场近似下的度规柱对称解,分析了此解的性质.     

关于正定张量定义和二阶张量特征向量

该文讨论了国内外数办学著作中出现的实质上有很大差异的两个正定张量定义。其一遵循数学的传统，将对称作为正定张量的先决条件，这样定义的正定张量与正定矩阵有很好的对应性；其二则不管该张量是否对称，直接由张量对任一向量的作用来定义是否正定。说明了这两个定义所定义的正定张量性质的不同，以及由此引起的张量极分解等定理叙述的不同。该文还阐明了对二阶对称张量成立的关于特征方程的重根与重向的一些结论对非对称二阶张量不一定成立。     

Hall Effect in Quasicrystals

The relations between Hall effect and symmetry are discussed for all 2- and 3-dimensional quasicrystals with crystallographical|y forbidden symmetries. The results show that the numbers of independent components of the Hall coefficient (R11) are one for 3-dimensional quasicrystals, two for those 2-dimensional quasicrystals whose symmetry group is non-Abelian, and three for those 2-dimensional quasicrystals whose symmetry group is Abelian. respectively. The quasicrysta[s with the same number of independent components have the same form of the components of R11.     

DKDP晶体的固-固生长

本文描述 DKDP 晶体的固一回生长现象。它可以在四方母体上发生,也可以在单斜母体上发生。固一固生长过程与母相晶体的对称性有关,与周围的介质无关。测量了不同温度下的生长速度,对固一固生长的机制进行了讨论。     

Strained silicon as a new electro-optic material

For decades, silicon has been the material of choice for mass fabrication of electronics. This is in contrast to photonics, where passive optical components in silicon have only recently been realized. The slow progress within silicon optoelectronics, where electronic and optical functionalities can be integrated into monolithic components based on the versatile silicon platform, is due to the limited active optical properties of silicon. Recently, however, a continuous-wave Raman silicon laser was demonstrated; if an effective modulator could also be realized in silicon, data processing and transmission could potentially be performed by all-silicon electronic and optical components. Here we have discovered that a significant linear electro-optic effect is induced in silicon by breaking the crystal symmetry. The symmetry is broken by depositing a straining layer on top of a silicon waveguide, and the induced nonlinear coefficient, chi(2) approximately 15 pm V(-1), makes it possible to realize a silicon electro-optic modulator. The strain-induced linear electro-optic effect may be used to remove a bottleneck in modern computers by replacing the electronic bus with a much faster optical alternative.     

A voltage-gated ion channel model inferred from the crystal structure of alamethicin at 1.5-A resolution

The crystal structure of alamethicin in nonaqueous solvent has been determined, and refined at 1.5-A resolution. The molecular conformation of the three crystallographically independent molecules is largely alpha-helical with a bend in the helix axis at an internal proline residue. The helix structure is highly amphipathic as most of the solvent-accessible polar atoms lie on a narrow strip of surface parallel to the helix axis. Molecular models for the voltage-gated ion channel, with n-fold symmetry and based on the molecular conformations observed in the crystal, are characterized by strong surface complementarity, a hydrophilic interior and a hydrophobic exterior. The channel structures are stabilized by a hydrated annulus of hydrogen-bonded glutamine residues which produce the greatest restriction in the channel diameter.     

组态相互作用中的特征波函数

通过实例说明特征组态相互作用方法（ＣＤＣＩ）的基本原理，该方法充分运用组态相互作用中的点群对称与自旋对称，从各组态相互关联中找出最小数目的线性无关组态—特征组态（ＣＤ）．ＣＤＣＩ方法简化了ＣＩ的计算过程，对于高对称点群更加显示了它的优越性．     

C_(2v)对称的d~4(d~6)电子组态哈密顿矩阵

本文未采用任何可调参量实验拟合的方法,直接得出含Trees改正在内的C_(2v)对称d~4(d~6)电子组态的哈密顿矩阵元。从理论上解决了计算凡具有这种性质离子的晶场吸收光谱,确又避免了结果的任意性。     

石英谐振器力灵敏度温度系数特性分析

力灵敏度温度系数是石英谐振器产生温漂的主要原因之一，而且这种温漂不能用差频方法消除，因此，它是影响石英谐振式力传感器测量精度的主要原因．文中给出了测量误差与力灵敏度温度系数之间的定量关系，并得到实验验证．阐述了力灵敏度温度系数的物理意义，分析确定了标定温度的方法．在一定温度范围内使用的石英晶体谐振器，既要有一定的分辨率，又要使其测量结果不受温度影响，为此提出了石英谐振器最佳取向选取原则．根据这一原则，找出了ＡＴ切型晶片用作力敏元件时的最佳施力方位角．为提高石英谐振式力传感器的测量精度提供了一个理论基础．     

光电二极管物理特性组合测量仪及测试

研究制作测试光电管、二极管物理特性仪器并完成数据测试，提高仪器设备的综合性。采用建筑装修材料铝方管材制作光电管暗箱，用数字表头数码管改装成电流表、电压表并与相关元件组装成具有对不同物理量进行测试的仪器，可分别测试出光电管的光电特性和晶体二极管的伏安特性。该仪器体积小，结构简单，可操作性强，测试出的数据满足物理实验与工程分析的要求。     

Crystal symmetry and the reversibility of martensitic transformations

Martensitic transformations are diffusionless, solid-to-solid phase transitions, and have been observed in metals, alloys, ceramics and proteins. They are characterized by a rapid change of crystal structure, accompanied by the development of a rich microstructure. Martensitic transformations can be irreversible, as seen in steels upon quenching, or they can be reversible, such as those observed in shape-memory alloys. In the latter case, the microstructures formed on cooling are easily manipulated by loads and disappear upon reheating. Here, using mathematical theory and numerical simulation, we explain these sharp differences in behaviour on the basis of the change in crystal symmetry during the transition. We find that a necessary condition for reversibility is that the symmetry groups of the parent and product phases be included in a common finite symmetry group. In these cases, the energy barrier to lattice-invariant shear is generically higher than that pertaining to the phase change and, consequently, transformations of this type can occur with virtually no plasticity. Irreversibility is inevitable in all other martensitic transformations, where the energy barrier to plastic deformation (via lattice-invariant shears, as in twinning or slip) is no higher than the barrier to the phase change itself. Various experimental observations confirm the importance of the symmetry of the stable states in determining the macroscopic reversibility of martensitic transformations.