一个新的平面不可压缩的Navier-Stokes方程的八模类Lorenz方程组截断

通过对平面正方形区域上不可压缩的Navier-Stokes方程进行傅立叶展开后截断得到一个新的八模类Lorenz方程组,给出了该方程组的定常解及吸引子存在性和全局稳定性的证明。同时,数值模拟了雷诺数在一定范围内变化时方程组的基本动力学行为和混沌轨线。系统通过一系列的分岔展现了复杂的随机行为。     

双曲对称中的分形集

目的将分形集通过双曲变换压缩入双曲极限圆中,构造具有分形特性的极限圆图案.方法分析双曲对称群的特点,改造欧式平面上构造经典分形的IFS迭代函数系,利用这种迭代函数系与双曲平面对称变换构造出组合IFS,通过随机挑选组合IFS中的仿射变换,构造双曲排列的分形集.结果实现了将欧式平面的经典分形集以及普通的汉字压缩到了双曲平面上.结论笔者所提出的构造技术可以用于生成包含经典分形的双曲对称图案以及双曲对称排列的汉字艺术图案.     

非线性动力学理论在反应堆噪声分析中的应用研究

利用非线性动力学理论，给出了反应堆噪声功率振荡的非线性特性的差别方法，并对实际信号进行了处理。结果表明热态模拟运行时，反应堆的功率振荡易发生Hopf分叉，圆周形吸引子是存在的，随机噪声会对维数产生较大的干扰，但基本未改变吸引子的形状。该方法对反应堆的详细分析有一定的实际意义。     

气液两相流确定性混沌分析

采用确定性混沌理论研究了空气 水两相流压力和压差信号的重构相空间、吸引子不变量的规律。结果表明 ,气液两相流是 1个低维混沌动力学系统 ,各流型间的非线性动力学特性不同。气液两相流的吸引子不变量 ,如Hurst指数、关联维数和Kolmogorov熵等都与流型关系密切。在多数流型内参数波动具有持久性特征 ,首次发现了高气速环状流区的反持久特征。     

用作气体动压轴承的微晶碳化硼材料

通过采用搅动高能球磨工艺制得粒度<1μm的微细B_4C粉;采用物理、化学方法提纯原始D_4C微细粉末,通过严格控制热压温度、压力与时间制得了密度为2.50～2.52g/cm~3,Knoop硬度为3300～4000,平均晶粒度<1.0μm的高性能微晶B_4C材料,该材料性能在原有基础上得到较大提高,可满足气体动压轴承苛刻的加工精度与装配精度要求。     

Lorenz和Rossler混沌系统的两驱动一响应同步研究

本文对Lorenz吸引子和Rossler吸引子的两变量驱动一变量同步现象进行了深入研究．结果表明，Lorenz吸引子可任意实现两变量驱动一变量同步，而Rossler吸引子只能有选择地实现两变量驱动一变量同步．本文由Rossler吸引子发展了同步概念．     

Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method

Our aim in this article is to study a new method for the approximation of the Navier-Stokes equations, and to present and discuss numerical results supporting the method. This method, called the nonlinear Galerkin method, uses nonlinear manifolds which are close to the attractor, while in the usual Galerkin method, we look for solutions in a linear space, i.e., whose components are independent. The equation of the manifold corresponds to an interaction law between small and large eddies and it is derived by asymptotic expansion from the exact equation. We consider here the two- and three-dimensional space periodic cases in the context of a pseudo-spectral discretization of the equation. We notice however that the method applies as well to more general flows, in particular nonhomogeneous flows.     

对称混浊及其计算机可视性图象

本文研究一种对称的混沌现象。给出一类具有优美对称性质的对称混沌映射，探讨其对称混沌吸引子以及混沌区域可视化的方法。研究对称混沌的可视化，有助于把握混沌系统的性质，并可用于花型图案设计。     

Color Characterization and Balancing by a Nonlinear Line Attractor Network for Image Enhancement

A novel method to map high dynamic range scenes to low dynamic range images utilizing the concept of color characterization, enhancement, and balancing is described in this letter. Each pixel of the image is first characterized by extracting the relationship of the red, green, and blue components along with its corresponding neighbors using a nonlinear line attractor network to form an associative memory. Then, the illumination enhancement process is performed using a hyperbolic tangent function to provide dynamic range compression to each pixel in the image. The slope of the hyperbolic tangent function is controlled using a parameter that is determined by the local and global statistics of the image to facilitate the change of the intensity level. A color balancing process restores the original color characteristics of the image based on learned associative memory matrices which eliminate image distortion due to improper recombination of red, green and blue components after enhancement. Experiments conducted on images captured at extremely uneven lighting environments show that the proposed method outperforms other image enhancement algorithms.     

分形在信息处理中的应用

分形是一门新兴的信息数学理论,具有广泛的应用价值。文中对分形原理及其实现算法做了分析和研究,阐述了其迭代函数系,总结了分形在信息处理中的一些应用。并利用分形吸引子对一些图形、数据等信息进行了处理。仿真实验表明,运用分形方法来处理信息可以有效地获得原始信息的纹理特征。