A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

在不同激光脉宽下的高次谐波

用数值计算方法计算了不同强激光脉冲宽度下高次谐波的产生.我们发现对于激光场强度不高,不能有效电离初态的激光场,长脉冲宽度可以更有效产生高次谐波;而对于高场强的激光场,由于它能够在几个光学周期之内把原子的初态全部电离,所以短脉冲的激光场能够更有效产生高次谐波.     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

双折射滤光片的色散特性研究

研究了由理想线偏振片和单轴双折射晶体波片组成的双折射滤光片倾斜放置时的二阶色散和 三阶色散特性，包括波片厚度、光线入射角和光轴旋转角的变化对二阶和三阶色散的影响. 还给出了双折射滤光片的群延迟表达式，并就色散特性与GT干涉仪进行了详细比较. 关键词： 双折射滤光片 群延迟 二阶色散 三阶色散     

Probability Interpretation of the Integral of Fractional Order

We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.     

A Triangle Inequality for Measurement

We introduce the triangle inequality for measurement. This is a property that when satisfied by a measurement enables one to construct a metric on the set of elements with measure zero that yields the relative Scott topology. The naturality of this construction permits a categorical solution to the model problem in domain theory for locally compact metric spaces. The first time such a solution has been achieved.     

Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions

This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.

     

非线性光纤环形镜的脉冲透过特性研究

研究了光纤反常色散区非线性环形镜（NOLM）的脉冲透过特性，得到NOLM周期性透过率函数 第一极大值处透过率、压缩比和对应的孤子阶数与环长之间的函数关系图.通过比较长环和 短环NOLM对无啁啾、啁啾脉冲的透过率和压缩比特性，得出了长环有利于脉冲整形而短环有 利于脉冲压缩的结论. 关键词： 非线性环形镜 透过率 压缩比 孤子阶数