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     

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.     

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.     

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.     

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.     

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.     

Yangian symmetries and integrability of the Dirac equation with spin symmetry

We show that a Yangian symmetry, namely, Y(su(2))$Y\left(su\left(2\right)\right)$, exists in the Dirac equation with spin symmetry when the potential term takes a Coulomb form. We construct the generators of Y(su(2))$Y\left(su\left(2\right)\right)$ explicitly and get the energy spectrum of this model from the representation theory for Y(su(2))$Y\left(su\left(2\right)\right)$. We also show that this model is integrable, from RTT relations.     

Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering

Using total light scattering technique to measure the particle size distribution has advantages of simplicity in measurement principle and convenience in the optical arrangement. However, the calculation of extinction efficiency based on Mie theory for a spherical particle is expensive in both time and resources. Thus, a simple but accurate approximation formula for the exact extinction efficiency may be very desirable. The accuracy and limitations of using the anomalous diffraction approximation (ADA) method for calculating the extinction efficiency of a spherical particle are investigated. Meanwhile, the monomodal and bimodal particle size distributions of spherical particles are retrieved using the genetic algorithm in the dependent model. Furthermore, the spheroidal model in the retrieval of non-spherical particle size distribution is also discussed, which verifies the non-sphericity has a significant effect on the retrieval of particle size distribution compared with the assumed homogeneous isotropic sphere. Both numerical computer simulations and experimental results illustrate that the ADA can be successfully applied to retrieve the particle size distributions for spherical and spheroidal particles with high stability even in the presence of random noise. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.     

A radial analogue of Poisson’s summation formula with applications to powder diffraction and pinwheel patterns

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.     

Compression of silver in a diamond anvil cell: Pressure dependences of strength and grain size from X-ray diffraction data

Two silver samples, coarse grained (c-Ag, grain size 300±30 nm) and nanocrystalline (n-Ag, grain size 55±6 nm), are compressed in a diamond anvil cell in separate experiments. The pressure is increased in steps of ∼3 GPa and the diffraction pattern recorded at each pressure. The grain size and compressive strength are determined from the analysis of the diffraction line-widths. The grain size of c-Ag decreases rapidly from 300±30 nm at ambient pressure to 40±8 nm at 15 GPa, and then gradually to 20±3 nm at 40 GPa. After pressure release to ambient condition, the grain size is 25±4 nm. The strength at ambient pressure is 0.18±0.05 GPa and increases to 1.0±0.3 GPa at 40 GPa. The grain size of n-Ag decreases from 55±6 nm at ambient pressure to 17±4 nm at 15 GPa and to 14±3 nm at 55 GPa. After release of pressure to ambient condition, the grain size is 50±7 nm. The strength increases from 0.51±0.07 GPa at ambient pressure to 3.5±0.4 GPa at 55 GPa. The strength is found to vary as the inverse of the square-root of the grain size. The results of the present measurements agree well with the grain-size dependence of strength derived from the hardness versus grain size data at ambient pressure available in the literature.     

最小二乘法在单缝衍射测波长中的应用

针对单缝夫琅禾费衍射实验,提出了用最小二乘法对测量到的衍射图像相对光强分布进行二次曲线拟合,并由拟合得到的数学表达式确定衍射条纹的精确位置．通过用最小二乘法与非最小二乘法对同一测量数据的处理结果进行比较,结论表明,用最小二乘法处理数据,可明显提高单缝夫琅禾费衍射方法测量光波波长的精度。     

Kepler方程的共形不变性、Mei对称性与守恒量

研究Kepler系统在无限小变换下的共形不变性、Mei对称性.给出该系统与总能量、角动量不同的新守恒量.并在广义坐标和广义速度构成的空间中讨论这些守恒量的独立性.     

干涉、衍射实验中衍射物位置的估算

从光源的空间相干性和实际光源的边缘衍射特性两个方面分析给出了干涉、衍射实验中衍射物到光源的距离的估算公式,分析了双缝干涉和泊松亮斑两个实验实例.