相干反斯托克斯拉曼及相干反斯托克斯超拉曼光谱微观极化率张量元的简化方案-C_(∞v)对称性

相干反斯托克斯拉曼光谱(CARS)和四阶相干反斯托克斯超拉曼光谱(CAHRS)广泛应用于分子界面和生物膜表面的研究。然而,高阶非线性光学过程中分子微观极化率张量元数量众多,关系复杂,使研究者对CARS和CAHRS很难进行定量分析。采取以下方案对属于C_(∞v)对称性的分子基团的CARS和CAHRS的微观极化率张量元进行简化。首先将CARS微观极化率张量元β_(i′j′k′l′)表示成拉曼微观极化率张量元微分α′_(i′j′)的乘积,CAHRS微观极化率张量元β_(i′j′k′l′m′)表示成超拉曼微观极化率张量元微分β′_(i′j′k′)和拉曼微观极化率张量元微分α′_(i′j′)的乘积,再利用α′_(i′j′)之间的比值及β′_(i′j′k′)之间的比值得到β_(i′j′k′l′)和β_(i′j′k′l′m′)之间的比值。使用这些CARS和CAHRS微观极化率张量元之间的关系,能够得到CARS和CAHRS光谱的广义取向泛函及其广义取向参数,进而对界面分子取向信息进行定量分析。

基于键极化加和模型及其实验修正方法的超拉曼微观极化率张量元微分的简化方案-C_(2v)对称性

相干反斯托克斯拉曼光谱(CARS)和相干反斯托克斯超拉曼光谱(CAHRS)等高阶非线性光谱技术已经应用在动力学过程、基因表达谱筛选、高分辨率光谱分析等诸多领域。但因其涉及到的高阶微观极化率张量元数量众多,对其光谱信号进行定量分析非常困难。文献通过理论分析将CARS和CAHRS的微观极化率张量元分解为拉曼微观极化率张量元微分α′i′j′和超拉曼微观极化率张量元微分β′i′j′k′的乘积,将高阶光谱定量分析的困难简化为对低阶光谱的分析。该研究处理了具有C_(2v)对称性分子基团,提出一种利用键极化加和模型及其实验修正的方法简化超拉曼微观极化率张量元微分β′i′j′k′比值的方案。首先利用键极化加和模型方法,在对C_(2v)分子基团局域模式假设的基础上,进行单键的局域模式假设,通过对单键伸缩振动进行简正振动模式的分析,并与单键的偶极矩表达式进行比较,得到单键的超拉曼微观极化率张量元微分β′i′j′k′。在单键β′i′j′k′结果的基础上利用键极化加和模型,对C_(2v)分子基团进行对称性分析,将基团中两个单键伸缩振动的β′i′j′k′耦合,得到C_(2v)分子基团对称振动和反对称振动两种简正振动模式的超拉曼微观极化率张量元微分β′i′j′k′的表达式。在此基础上对C_(2v)分子基团对称振动和反对称振动的β′i′j′k′表达式进行理论推导,结合对应振动模式下不同偏振组合的超拉曼退偏率ρHR-SS和ρHR-AS及HV偏振组合时实验测量的超拉曼光谱强度比,得到超拉曼实验修正的C_(2v)分子基团β′i′j′k′之间的比值。再结合文献中拉曼实验修正的拉曼微观极化率张量元微分α′i′j′之间的比值,即可得到C_(2v)分子基团CARS和CAHRS的微观极化率张量元之间的比例关系,为定量分析高阶非线性光谱信息提供理论基础。

相干反斯托克斯拉曼及相干反斯托克斯超拉曼光谱微观极化率张量元的简化方案-C3v对称性

相干反斯托克斯拉曼光谱(CARS)和四阶相干反斯托克斯超拉曼光谱(CAHRS)已经广泛应用于分子的光谱特性、肿瘤细胞的结构及分子反应动力学等问题的研究。对这种复杂的高阶非线性光谱进行定量分析所面临的主要难题是高阶非线性光学过程中分子微观极化率张量元数量众多,关系复杂。在前期报道的C∞v对称性分子基团的CARS和CAHRS的微观极化率张量元简化方案的基础上,对分子对称性更加复杂的C3v对称性的分子基团的CARS和CAHRS的微观极化率张量元进行简化,为定量分析C3v对称性分子基团的CARS和CAHRS光谱信息提供必要的理论基础。首先将CARS微观极化率张量元βi′j′k′l′表示为拉曼微观极化率张量元微分α′i′j′的乘积,CAHRS微观极化率张量元βi′j′k′l′m′表示为超拉曼微观极化率张量元微分β′i′j′k′和拉曼微观极化率张量元微分α′i′j′的乘积。用α′i′j′和β′i′j′k′之间的比值关系简化βi′j′k′l′和βi′j′k′l′m′之间比值。对于C3v对称类型分子基团的对称振动模式A1,9个非零且3个独立的CARS微观极化率张量元可以用α′i′j′之间的1个比值参数R^RSS进行描述,21个非零且6个独立的CAHRS微观极化率张量元可以用α′i′j′之间及β′i′j′k′之间的3个比值参数R^RSS,R^HRSS,1和R^HRSS,2进行描述。然后利用键极化加和模型方法,通过计算C3v对称性分子基团中的各个单键与单键之间的耦合关系,得到C3v对称性分子基团的对称伸缩振动模式A1所对应的所有超拉曼微观极化率张量元微分β′i′j′k′分量的比值,结合文献中给出的拉曼微观极化率张量元微分α′i′j′分量的比值,进一步简化C3v对称性分子基团CARS和CAHRS微观极化率张量元之间的关系。从这些简化了的CARS和CAHRS微观极化率张量元之间的关系,可以进一步简化CARS和CAHRS信号及广义取向泛函RIJK(θ)的表达式,得到RIJK(θ)随界面分子基团取向角度θ的变化规律。此外,也详细推导了C3v对称性分子基团对射式实验构型CAHRS过程的强度因子dIJK、广义取向泛函RIJK(θ)及广义取向参数c2和c4的表达式,为定量分析界面分子取向信息奠定了理论基础。

Raman散射张量(作为统一张量)元的选择定则

Ｒａｍａｎ散射张量（作为统一张量）元的选择定则郝伟廖理几金泽宸＊刘凤艳（北京工业大学应用物理系北京１０００２２）（＊中国农业大学基础科技学院北京１０００９４）ＳｅｌｅｃｔｉｏｎＲｕｌｅｓｆｏｒＲａｍａｎＳｃａｔｅｒｉｎｇＴｅｎｓｏｒａｓＵｎｉｆｉｅｄ...

基于偏振拉曼散射光谱的4H-SiC晶体各向异性特性研究

采用背向散射偏振配置,对半极性a面(1120)生长的4H-SiC晶体,测量了激发光偏振方向与光轴成不同角度时各声子振动的偏振拉曼散射光谱,研究了不同声子模式的偏振拉曼散射光的强度变化与性质。利用拉曼选择定则,对实验结果进行拟合分析得到了不同声子模式的拉曼散射矩阵张量元系数及其各向异性特征。研究结果为深入了解4H-SiC晶体的微观结构和各向异性性质提供依据。

Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method

Scalar CSAMT is only suitable for measurements in one and two dimensions perpendicular to geological structures. For complex 3D geoelectric structure, tensor CSAMT is more suitable. In this paper, we discuss 3D tensor CSAMT forward modeling using the vector finite-element method. To verify the feasibility of the algorithm, we calculate the electric field, magnetic field, and tensor impedance of the 3D CSAMT far-zone field in layered media and compare them with theoretical solutions. In addition, a three-dimensional anomaly in half-space is also simulated, and the response characteristics of the impedance tensor and the apparent resistivity and impedance phase are analyzed. The results suggest that the vector finite-element method produces high-precision electromagnetic field and impedance tensor data, satisfies the electric field discontinuity, and does not require divergence correction using the vector finite-element method.

Estimation of surface tension of organic compounds using quantitative structure-property relationship

A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.

Numerical Homogenization of the Elliptic Problem with Rapidly Varying Tensor or Boundary Condition

Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.

Construction of A Kind of Wavelets

A method to construct wavelets on invariant sets is given, which can he used to construct nontensor-type multiwavelets，