Analysis of Radiation Phenomena in a Wedge Ended Dielectric Slab Waveguide

Radiation phenomena observed in a wedge shape ended dielectric slab waveguide are analyzed using mode matching technique. The case of transverse electric polarization (TE) being parallel to dielectric slab waveguide is assumed. In order to describe the fields in the wedge region, a stack of dielectric plates is assumed and in each layer the fields are expanded in terms of the mixed spectrum of guided and radiated modes. A similar expansion is used in the constant thickness slab waveguide while in free space medium a continuous-radiation mode expansion is used. Then a mode matching approach is applied, incorporating the orthogonality properties of mixed spectrum modes, in order to compute the wave fields inside the dielectric slab waveguide and wedge medium. Mode matching is achieved by discretizing the continuous radiation mode spectrum leading into a numerically stable solution provided a sufficient large number of points are used to convert integrals into finite summations. Numerical computations are carried out for various wedge geometries and shapes including linear and exponential profiles.     

Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．     

类氢及碱金属原子激发态寿命的半经典计算公式

根据对应原理,得到了类氢原子能态平均寿命半经典的计算公式τ(n,l),然后利用相对论单通道量子数亏损理论进行推广,得到用来计算考虑总角动量J的激发态寿命公式τ(n,l,l+1/2)和τ(n,l,l-1/2),利用单通道量子数亏损理论得到了碱金属原子n、l远大于1时激发态寿命的半经典公式τ(n.l)=τ0(m+M/nm/v/+M)2v7l(l+1/2)/n4,其计算结果和实验数据符合的很好.     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

钙钛矿型La_((1 x)/2)Sr_((1-x)/2)Co_(1-x)Cu_xO_3催化CO氧化活性与表征

研究了钙钛矿型LaSrCoCu_xO_3催化剂对CO氧化反应的催化活性及其表面氧的催化作用．结果表明，x＝0．4的催化剂对CO氧化具有最高催化活性，常压及本实验条件下CO完全氧化的最低温度为168℃；催化剂均为氧缺陷化合物，吸附于表面晶格氧缺陷上的吸附氧是CO氧化反应的活性氧物种；并发现催化剂中存在有非常价态的C04 ，认为CO氧化反应是通过吸附氧调变Co3 和Co4 价态而进行．     

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

One‐Dimensional,Cofacial Porphyrin Polymers Formed by Self‐Assembly of meso‐Tetrakis(ERE Donor) Zinc(II) Porphyrins

A series of meso‐tetrakis‐(ERE donor) zinc(II) porphyrins n Zn (ERE donor=4‐R‐3,5‐bis[(E)‐methyl]phenyl; 1 Zn: E=NMe₂, R=Br; 2 Zn: E=NMe₂, R=H; 3 Zn: E=OMe, R=Br; 4 Zn: E=OMe, R=H) have been synthesized in excellent yields. As a result of the combination of a Lewis acidic site and eight Lewis basic sites within one molecule, monomeric molecules of n Zn self‐assemble to form one‐dimensional porphyrin polymers [ n Zn]_∞ in the solid state, as confirmed for 1 Zn and 3 Zn by X‐ray crystallography. The coordination environment around the zinc(II) ions in these polymers is octahedral. They are ligated by four equatorial nitrogen atoms of the porphyrin and two apical E atoms (E=N, O) provided by the EBrE donor groups of adjacent n Zn molecules. Complexes 2 Zn and 4 Zn did not form single crystals, but solid‐state UV/Vis analysis points to the formation of similar structures. Solution UV/Vis and ¹H NMR spectroscopy indicated that interactions between 1 Zn and 2 Zn monomers in the polymers are stronger than between 3 Zn and 4 Zn monomers. Interestingly, they also revealed that the presence of a neighboring bromine atom in the EBrE donor groups has a considerable influence on the coordination properties of the benzylic N or O atoms. The zinc(II) ions of the porphyrins most likely adopt only hexacoordination in the solid state, owing to the unique predisposition of Lewis acidic and basic sites in the n Zn molecules. Several parameters of the aggregates, for example, the interplanar separation between porphyrins and the zinc–zinc distances, change as a function of the coordinating E groups. The high degree of modularity in their synthesis makes these zinc(II) porphyrins an interesting new entry in noncovalent multiporphyrin assemblies.