Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.     

X-ray diffraction from single Al6CuLi3 grains showing five-fold symmetry

We present here the detailed results of X-ray diffraction from single quasicrystals of Al₆CuLi₃. X-ray precession photographs taken down the two-, three- and five-fold axes along with rotation and zero-level Weissenberg photographs are shown. Preliminary analysis of the diffraction data rules out the twin hypothesis.     

Lie point symmetry algebras and finite transformation groups of the general Broer--Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer--Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.     

衍射散射式颗粒粒度测量法的研究新进展

介绍了衍射散射式颗粒粒度测量法的基本光路结构和理论模型,讨论了决定其性能优劣的重要指标--测量下限,对影响测量下限向小粒径范围延伸的参数进行了分析.继而介绍了近年来国内外主要粒度仪品牌在光学结构和散射理论模型方面所做的改进,阐述了它们的工作原理和性能特点.最后对衍射散射式颗粒粒度测量法的发展前景做出了展望,从修正理论模...     

Study of the symmetry of single-wall nanotubes by electron diffraction

Determining precisely the atomic structure of single-wall carbon nanotubes is essential since it tailors electronic properties of this new carbon material. Here, we present a quantitative electron diffraction study of electric-arc produced single-wall carbon nanotube bundles, combined with simulations based on the kinematic theory and with real-space images. We stress the importance of the twist of the bundle in the interpretation of our data and we analyze both packing lattice parameters and chirality distribution. We show that, within a given bundle, no chirality is favoured whereas SWNT diameters are almost uniform. Received 5 February 1999     

Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.     

离散变质量完整系统的Noether对称性与Mei对称性

本文研究离散变质量完整系统的Noether对称性与Mei对称性.首先用差分离散变分的方法,建立起离散变质量完整系统的运动方程和能量演化方程.然后给出该系统的Noether对称性和Mei对称性的定义及离散Noether守恒量的形式.得到系统的Noether对称性与Mei对称性导致离散Noether守恒量的条件.最后举例说明结果的应用.     

构造Birkhoff表示的Hojman方法与Birkhoff对称性

讨论了构造Birkhoff表示的Hojman方法.利用该方法重新研究Birkhoff对称性,提出一种关于该对称性的新见解,给出Birkhoff守恒量的新证明,并对该守恒量仅与Birkhoff张量相关作出解释.举例说明所得结果的应用.     

Pixel size and pitch measurements of liquid crystal spatial light modulator by optical diffraction

We present a simple technique for the determination of pixel size and pitch of liquid crystal (LC) based spatial light modulator (SLM). The proposed method is based on optical diffraction from pixelated LC panel that has been modeled as a two-dimensional array of rectangular apertures. A novel yet simple, two-plane measurement technique is implemented to circumvent the difficulty in absolute distance measurement. Experimental results are presented for electrically addressed twisted nematic LC-SLM removed from the display projector.     

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.     

闪耀光栅光强分布的一种求解方法

以反射式闪耀光栅为例,提出了一种根据多孔夫琅禾费衍射性质来计算闪耀光栅夫琅禾费衍射光强分布的方法,得到的结果和教材完全一致.     

Chiral symmetry restoration and properties of Goldstone bosons at finite temperature

We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-) Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In chiral limit, the pion and its partner sigma degenerate at the critical temperature begin{document}$T_{rm c}$end{document}. At begin{document}$T gtrsim T_{rm c}$end{document}, it was found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover, which is consistent with that obtained by the maximum point of chiral susceptibility. A parallel analysis for kaon and pseudoscalar begin{document}$ sbar{s} $end{document} suggests that heavy mesons may survive above begin{document}$T_{rm c}$end{document}.     

A method of suppression of diffraction oscillations near the diffraction reflection region

Light propagation through the layer of a chiral photonic crystal with graded parameters of modulation is considered in the case of oblique incidence. The problem is solved by the Ambartsumian’s layer addition method. It is shown that under certain conditions it is possible to suppress the diffraction oscillations near the diffraction reflection region.     

横梁弯曲衍射法测玻璃杨氏模量的改进

设计、制作了横梁弯曲衍射法测物质材料的杨氏模量仪器,并利用单缝衍射测量了火石玻璃挠度的变化,实现了螺旋加力装置配合拉力传感器对拉力连续、稳定控制.     

Mathematical method to predict the diffraction efficiency of holograms

In this paper, a method is presented which uses a multi-factorial decision model of fuzzy-set theory to predict the diffraction efficiency of holograms. A prediction fitting rate of 85% has been obtained. This method can be used as a guide to processing holograms.     

弱谐波情况下透射光栅衍射效率标定方法

同步辐射光源中的高次谐波会使透射光栅衍射效率标定精度变差。为了校正光源中的高次谐波对透射光栅衍射效率标定的影响,提出了一种光源存在弱谐波情况下的透射光栅衍射效率标定方法,通过使用谐波X射线的衍射效率修正基波衍射效率标定中谐波的影响,从而得到更为准确的透射光栅衍射效率。使用该标定方法在北京同步辐射光源上开展了透射光栅相对衍射效率标定工作。实验结果表明:在100~800eV存在高次谐波能段,修正后透射光栅一级与零级的相对衍射效率与理论模拟结果吻合较好,修正后光栅二级与一级的相对衍射效率更接近理论模拟结果,但与理论模拟结果仍有较大偏差,该偏差主要来源光栅较弱的二级衍射。     

衍射增强成像提取多种信息的简便方法研究

衍射增强相位衬度成像中的信息分离研究一直以来都是相关研究人员重点关注的方向之一. 本文在利用余弦函数拟合衍射增强成像中的摇摆曲线的基础上, 推导出了峰位像、左腰像和右腰像的余弦函数表达式以及吸收像、折射角像和散射角方差像的解析表达式, 形成了一种基于衍射增强成像的简便信息分离方法. 该方法只需利用摇摆曲线左腰、右腰和峰位三幅图像, 就能提取出样品的吸收、折射和散射信息, 具有方法简便、样品所受辐射剂量低等优点. 对模型样品和真实样品的实验结果表明, 本文所提方法可成功对样品进行信息分离, 并且所获得的信息分离结果可以和目前常用的多图统计方法(至少需要7张图像)获得的实验结果相比较. 关键词： 衍射增强成像 相位衬度成像 样品信息提取     

X射线衍射多相谱中某一物相点阵参数的直接求解方法

介绍了一种新的求解点阵参数的方法--不涉及结构的谱峰拟合方法.该方法适用于单一物相或多个物相衍射谱中某一物相点阵参数的直接求解,可以避免外推函数的不同选择而造成的差异,且快速准确.根据此方法编写的应用程序已在实际工作中得到应用.程序中还包括了调整样品表面离轴偏差和零度偏差以提高拟合精确度的功能. 关键词： X射线衍射 谱峰拟合 点阵参数     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.