软物质准晶广义流体动力学的一个应用——圆柱绕流的近似解

文中报道了笔者建议的软物质准晶广义流体动力学的一个应用——软物质准晶圆柱绕流的近似解.人们熟知,在普通流体动力学中, 二维圆柱绕流问题遇到很大的困难,Stokes求解它,未能成功,这就是著名Stokes佯谬.为了克服这一困难, Oseen分析了原因不在边界条件的提法,也不在Stokes的求解,问题出在Navier-Stokes方程, 他对方程进行了修改, 得到了二维绕流问题的有物理意义的近似分析解.本文借助于Oseen的方法讨论12次对称软物质准晶广义流体动力学二维绕流问题.由于问题比普通流体动力学复杂得多,严格的求解,在目前的条件下是根本不可能的.笔者提出一种近似方法——交替程序去构造其零级近似解,并且把该结果用于软物质准晶的位错问题.     

A method of quenching in fusing state under high static pressure used to study quasicrystals

Abstract

In this paper, a new method of quenching in fusing state under high static pressure (MQFSHP), which was developed in the beginning of 1986 by our group^1,2, used to study quasicrystals in alloys has been introduced.     

十二重准晶中的方向缺陷

采用多重散射的方法研究了十二重准晶中的缺陷模,发现在十二重准晶中存在方向缺陷,且当缺陷组合围绕对称中心旋转时,在保持原有缺陷模的基础上,出现了新的缺陷模. 关键词： 准晶 缺陷 带隙     

Solutions for hydrodynamics of 5- and 10-fold symmetry quasicrystals

This study carries out a complete analysis of time-space solution of hydrodynamics of pentagonal/decagonal quasicrystals. The behaviors of wave propagation for phonons and diffusion for phasons and coupling between phonon-phason fields are explored explicitly. Comprehensive discussion on physical time-space variations of all hydrodynamic field variables of the alloy quasicrystals is given. The computational specimen is simple, convenient in testing computational results, and provides a possibility that is easy to test experimentally. The quantitative results of mass density, viscosity velocities, phonon displacements, phason displacements, phonon stresses, phason stresses, viscosity stresses, and their time-space variations help us understand the motion of solid quasicrystals in a hydrodynamic condition (long-wavelength and low-frequency). The analysis presented in this paper can be used for octagonal and dodecagonal quasicrystals and is easily extended to other two-dimensional quasicrystals and three-dimensional icosahedral quasicrystals. Some problems explored by the computational results are also discussed.     

SH波对一维六方准晶中直裂纹的散射

分析了SH波对一维六方准晶中直裂纹的散射问题。利用积分变换技术,结合Copson方法,通过求解对偶积分方程,得到声子场和相位子场应力、位移及裂纹尖端动应力强度因子的解析表达式。通过数值算例讨论了裂纹长度、入射角和入射波频率对标准动应力强度因子的影响,此研究在工程材料应用中有一定的参考价值。     

包层空气孔渐变的准光子晶体光纤的色散特性研究

设计了一种准光子晶体光纤,其包层由呈准周期分布的空气孔构成,其中靠近芯区的空气孔的直径是渐变的.采用带有良匹配层(APML)吸收边界的全矢量频域有限差分(FDFD)方法对其色散特性进行了数值分析,计算了孔间距取1.5μm～2.2μm,最小空气孔直径分别取0.4μm～0.6μm,从第一层到第三层直径线性递增量分别为0.1μm和0.2μm的条件下,这种光纤基模的色散曲线.结果表明:通过调节包层中三种不同尺寸的空气孔的大小以及孔间距这四个参数,可以得到不同平坦水平的色散曲线,甚至于超低超平坦的色散曲线.例如,当孔间距取1.7μm,空气孔直径分别取0.5μm、0.7μm、0.9μm,在1.4μm～1.7～m波段内,这种光纤的色散值可以控制在6.0±3.0 ps/km.nm范围内.     

平面准晶中的路径守恒积分及其应用

目的 建立平面准晶中能量型路径守恒积分及其对偶形式,并确定准晶裂纹体裂尖应力奇异性阶数。方法,建立对过程中利用了平面准晶弹性理论的基本控制方程和高斯定理。结果与结论 给出了平面准晶体在静态,动态和运动裂纹情形时的路径守恒积分及其对偶形式,给出了守恒性证明,得到准晶裂纹体裂尖应力具有－１／２奇异性,与解析结果相符。     

Asymptotic solution to a nonlinear diffusion process by Chien-Latta's method

In this paper, by using Chien Wei-zang — Latta's composite expansion method^[5], we have obtained the first-order asymptotic solution to a system of equations for a nonlinear diffusion process, thus simplifying and improving the previous work^[4] considerably. Moreover, a kind of complete analytical solution has been given for a special case, and the periodic solution at the bifurcation point has been discussed, the related results being in agreement with the experiments.     

晶体和准晶旋声性质的旋转不变性

依据群论原理对计算张量的群论方法作了改进,采用非对称化基函数取代对称化基函数,以便于编程.用MATLAB编制了用于计算属于SO(2)群各阶张量的软件.借助于该软件得到了具有SO(2)群对称性的旋声张量的形式.指出晶体中属于六角系的6、6 mm和622晶类和准晶中属于五角系的5、52、5 m晶类的旋声性质具有围绕晶体或准晶中唯一高次轴的任意旋转不变性.该结果对于旋声性的应用有重要意义.