硅材料场致等效二阶极化率张量的研究

具有反演对称中心的硅单晶在电场作用下体内的反演对称中心消失,因而理论上应产生偶数阶非线性极化率。从理论上根据矢量与张量的作用,利用(eχf2f)=χ(3).E这一关系和张量变换理论系统地阐述了硅材料在内建电场或外加电场的作用下,具体在方向分别沿[111][、110]和[001]的电场作用下,得到的等效二阶极化率张量(eχf2f)分别与C3v、C2v和C4v点群的二阶极化率张量具有相同的形式,说明在物理性质方面,硅的对称性由Oh群在相应方向电场作用下分别被降低为C3v、C2v和C4v群,因此应该具有相应对称性晶体的二阶非线性光学性质;提出了电场E沿任意方向时硅的等效二阶极化率张量e(χf2f)的计算方法,对研究硅材料和其他具有反演对称中心材料的场致二阶非线性光学性质实验具有指导意义。     

C2+4的几何构型和Jahn-Teller效应

用从头计算法GCISD/6-311G*得到了C2+4分子的10种不同的几何构型,基中包括Cs,C∞v,C2v,D2h,D∞h,D4h,D2d,C3v等不同的构型.计算表明C2+4的Td构型不能稳定存在,详细讲座了Td构型的Jahn-Teller效应.讨论结果显示它们的各种畸变方式都符合群的分解原理,从而证明了C2+4分子的Td构型的Jahn-Teller效应非常明显.D4构型也存在Jahn-Teller效应.     

结构磁空间群C-G系数的计算

众所周知晶体空间群的C G系数在晶体学中有重要的意义。而磁空间群的C G系数尚无人计算。本文利用磁群共表示理论构造出磁空间群的不可约表示 ,进而利用本征函数法计算了O1 0h 结构磁空间群的C G系数。     

准晶体中八方晶系点群的对称性与矩阵表示

从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.     

对比分析三角Pr3+中心在CsCdBr3和GdCl3晶体中的能级分裂

以Racah的群表示论和Slater的波函数理论为基础,分别建立了4f2组态离子Pr3+在三角晶体场C3v和C3h中的91×91完全能量矩阵,并对Pr3+离子掺杂在卤化物CsCdBr3和GdCl3中的Stark能级做了计算与分析. 结果显示计算值与实验值吻合很好,表明在分析由稀土离子掺杂体系的能级分裂时,完全能量矩阵方法是有效的方法. 此外,将两种具有不同点群对称的体系的能级分裂情况作了比较,结果显示六阶晶体场参量对能级分裂的影响是不能忽略的,而且CsCdBr3:Pr3+和GdCl3:Pr3+将产生不同程度的畸变.     

对比分析三角Pr~(3+)中心在CsCdBr_3和GdCl_3晶体中的能级分裂

以Racah的群表示论和Slater的波函数理论为基础,分别建立了4f2组态离子Pr~(3+)在三角晶体场C3v和C3h中的91×91完全能量矩阵,并对Pr~(3+)离子掺杂在卤化物CsCdBr_3和GdCl_3中的Stark能级做了计算与分析.结果显示计算值与实验值吻合很好,表明在分析由稀土离子掺杂体系的能级分裂时,完全能量矩阵方法是有效的方法.此外,将两种具有不同点群对称的体系的能级分裂情况作了比较,结果显示六阶晶体场参量对能级分裂的影响是不能忽略的,而且CsCdBr_3:Pr~(3+)和GdCl_3:Pr~(3+)将产生不同程度的畸变.     

参数寻优支持向量机在基于光声光谱法的变压器故障诊断中的应用

为了解决变压器气相色谱分析法故障诊断中存在的操作繁琐、消耗待测气体和载气、检测周期长等缺点, 提出了利用光声光谱技术检测变压器油中CH4, C2H2, C2H4, C2H6, H2五种特征气体的含量并计算C2H2/C2H4, CH4/H2, C2H4/C2H6三对比值数据。将五种SVM类型和四种核函数采用交叉组合建立20种不同的支持向量机模型, 并采用启发式算法对于惩罚因子c和g的取值进行参数寻优, 以建立变压器故障诊断准确率最高、最快运行速度的支持向量机模型。启发式算法主要对比研究了粒子群算法和遗传算法在寻优精度与速度上的效果。仿真实验结果表明C-SVC模型、RBF核函数、遗传算法寻优构成的支持向量机模型对变压器故障的诊断准确率最高, 测试集达到97.5%, 训练集达到98.333 3%, 并且遗传算法的寻优速度快于粒子群算法2倍左右。该方法具有操作简单、非接触性测量、不消耗载气、检测周期短、稳定性和灵敏度高等优点。可以代替传统的气相色谱分析法进行变压器故障诊断, 满足变压器故障诊断的实际工程需要。     

O8h结构磁空间群C-G系数的计算

磁空间群相对于以往的空间群,在对物理图像的描述上更准确、更深刻。如它可在考虑晶体对称性的同时,也考虑到自旋磁矩的作用,因而它的C－G系数更加重要。本文利用本征函数法,计算了面心立方结构Oh^8磁空间群的C－G系数,以及波矢选择规则和C－G序列。     

D_(6h)~4结构空间群C-G系数的计算

在晶体拉曼散射张量的计算中 ,晶体空间群的C G系数具有重要作用 ,本文利用本征函数法[1] ,计算了六角密排结构D46h空间群的C G系数 ,同时给出波矢选择规则和C G序列。     

SiO2分子的基态(X1A1)结构与分析势能函数

应用群论及原子分子反应静力学方法推导了SiO2分子的电子态及其离解极限,采用B3P86方法,在6-311G**水平上,优化出SiO2基态分子稳定构型为单重态的C2V构型,其平衡核间距Re=RSi-O=0.1587 nm,∠OSiO=111.2°,能量为-440.4392 a.u..同时计算出基态的简正振动频率:对称伸缩振动频率v(B2)=945.4cm-1,弯曲振动频率v(A1)=273.5 cm-1和反对称伸缩振动频率v(A1)=1362.9cm-1.在此基础上,使用多体项展式理论方法,导出了基态SiO2分子的全空间解析势能函数,该势能函数准确再现了SiO2(C2V)平衡结构.     

Monte Carlo renormalization group Calculations for polymers

A simple method based on Wilson's renormalization group ideas is applied to calculate the dynamical critical exponentz for polymer chains in different dynamical regimes. It is shown that the Doi-Edwards reptating chain does not belong to the same dynamical universality class as the Rouse chain. The earlier results based on (4 –d, d space dimensionality) expansion for chains with excluded volume effect are recovered without any expansion. When combined with the Monte Carlo techniques, this method results in a simple scheme for calculating the static and dynamic exponents for a polymer chain with a prescribed dynamics. Numerical results suggest that the slithering snake model of Wall and Mandel for the dynamics is in a different dynamic universality class than the Rouse chain.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Research supported in part by the National Science Foundation (Grant No. DMR-8112968) and the Petroleum Research Fund, administered by the American Chemical Society.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

电光晶体研究究进进展及其对称性性研研究

由电场引起的晶体折射率的变化称为晶体的电光效应,具有电光效应的晶体称为电光晶体。利用电光效应可以制作电光Q开关等重要光电器件。晶体的电光效应及其有效利用,均与其对称性密切相关。本文在综述电光晶体研究进展的基础上,推导了不同晶系中各晶类电光效应类型及其特点,并以电光Q开关的要求为例讨论了晶体的电光效应及其对称性之间的关系。从讨论结果得出:立方晶系Td-ˉ43m,三方晶系C3v-3m,四方晶系D2d-4ˉ2m,D4v-4mm和六方晶系D3h-6ˉm2,C6v-6mm点群中相应电光系数的横向或纵向效应可能有实用价值。在考虑旋光性影响后,立方晶系T-23,三方晶系D3-32,四方晶系中S4-4ˉ,六方晶系中C3h-6ˉ等也有可能应用。但是,电光晶体的应用与许多因素相关,对称性只是其中一个基本条件。     

Invariants of three-manifolds from finite group cohomology

We compare on lens spaces the values of two topological invariants of three-manifolds, both built from a finite group G and a three-cocycle ω, which we conjectured to be equal up to a normalization. The first invariant is defined by triangulation—it is the partition function of the Dijkgraaf-Witten topological field theory—and the second one by surgery, using a quasi-Hopf algebra. When G is a cyclic group, we show that the first invariant reduces to a Gauss sum. Some identities satisfied by three-cocycles are derived in an appendix.     

硫醇自组装分子膜末端基团对其电荷输运特性的影响

在金(111)表面组装了具有不同末端基团的硫醇单层分子膜，并利用导电原子力显微镜研究了分子膜的电输运性质，发现不同末端基团的分子自组装膜的导电能力有明显差别.结合X射线光电子能谱，研究了末端基团中碳原子的结合能与相应硫醇分子电导的关系.结果表明不同末端基团分子膜导电能力的差别可归结为末端基团碳原子电子结合能的差异.结合能越高，末端基团电子的局域化程度越强，导致电子有效注入分子主链的势垒越高，从而减弱了分子膜对电子的输运能力.此外，实验还发现不同末端基团的硫醇单层分子膜有不同的表面电势，导致分子膜电流电压特性曲线的零点产生偏离. 关键词： 分子自组装膜 输运特性 末端基团 导电原子力显微镜     

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the timefrequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.     

具有四模式的低串扰及大群时延多芯微结构光纤的设计

针对光纤空分复用及模分复用传输系统中大容量和耦合串扰问题, 本文提出了一种具有四模式特性低串扰及大群时延的大容量多芯微结构光纤, 通过有限元法计算该光纤电磁场分布进而对其他参数进行分析. 结果表明: 合理的选定光纤结构参数, 可使得该光纤在C+L波段内同时实现19芯的LP₀₁, LP₁₁, LP₂₁, LP₀₂四个偏振模式的传输. 同时, 利用空气孔对电磁场较好的隔离作用来优化芯间串扰并得到较大的模式差分群时延及较为平坦的色散. 此外, 这种结构的光纤制作简单, 在短距离大容量的信息传递系统中具有重要应用.     

The symmetry group paradox for non-rigid molecules

In many situations, the energy levels for a quantum system, whose Hamiltonian is invariant under a specific symmetry group, are split when the Hamiltonian is replaced by a new one with lower symmetry. In non-rigid molecules (NRM), fast quantum tunnelling processes allow the molecule to change between different geometrical configurations related by permutations of identical nuclei (or with inversion as well), resulting in the splitting of the energy levels for the rigid molecule (RM) case where tunnelling is absent. However, for NRM, there is apparently a paradoxical situation where although the original RM energy levels are associated with a symmetry group isomorphic to the point group for the geometrical configuration, the split NRM energy levels are associated with a symmetry group consisting of all permutations and inversions related to the fast quantum tunnelling processes between configurations, and for which the point group is a subgroup. The resolution of this paradox, where energy level splitting is evidently accompanied by an enlargement of the symmetry group, is the subject of this article.     

Lack of the neighboring group rate effect in solvolytic reactions that proceed via participation

In order to investigate the influence of solvent polarity on the rate effect of double bonds in reactions that proceed via an extended π‐participation mechanism, the solvolysis rates (k_U) of the benzyl chloride derivative 1 and tertiary chloride 2 that have doubly unsaturated side chains were measured in absolute ethanol, 80% v/v. aq. ethanol and 97% wt. aq. trifluoroethanol. The rates of the corresponding saturated analogs 1S and 2S (k_S) were measured in 80% aq. ethanol and 97% wt. aq. trifluoroethanol, while those in pure ethanol were calculated according to LFER equation log k = s_f (E_f + N_f). In solvents with moderate ionizing power (ethanol and 80% aq. ethanol) the expected rate effects were obtained (k_U/k_S>1), while in solvent with high ionizing power (2,2,2‐trifluoroethanol) absence of the rate effect was observed (k_U/k_S≈1), indicating that in the k_S process the solvation of the transition state is very important, while in k_Δ process the breaking of the C? Cl bond is not appreciably developed in the transition state and the solvent effect is marginal. Copyright © 2007 John Wiley & Sons, Ltd.     

A statistical‐mechanical analysis of group additivity. Calculation of thermochemical values from frequency distributions

Molecular vibrational frequencies of homologous series plotted as cumulative frequency distributions are very similar, and the fine structure of the distributions exhibit identical features. An obvious explanation is that the changes in the molecular frequency distributions (MFDs) from one homologue to the next is independent of the chain length and of the functional groups in the molecule. Since group additivity is valid for the chosen homologous series there is here an explanation for the linearity of thermochemical values expressed by group additivity. For these properties the following hypothesis is proposed: group additivity is observed when the MFD is a sum of group frequency distributions (GFDs). This leads to additivity for the zero‐point vibrational energy which is confirmed by analysis of the frequencies of 126 organic molecules from 11 homologous series. The frequency distribution for a methylene group is estimated from that of octadecane. From this GFD combined with 11 different MFD it is possible to calculate model frequencies for the homologous series which are in good agreement with frequencies from ab initio calculations. For three thermochemical parameters (the logarithm of the vibrational partition function, the vibrational excitation energy and the vibrational heat capacity), the combination of the estimated methylene GFD with 11 different MFDs lead to group additivity values for a methylene group which are identical over a wide temperature range. The derivation of Benson additivity for thermochemical functions from frequency distributions is at step towards a better understanding of Benson additivity. Copyright © 2008 John Wiley & Sons, Ltd.