数字散斑相关测量方法的研究与改进

通过对数字散斑相关测量方法的研究,提出一种新的数字散斑相关搜索方法.采用该方法可大大节省数字散斑相关测量中数据处理的时间.实验表明,本文所提出的方法是一种实用的快速、高精度位移和变形的测量方法.     

木星“大红斑”的实验室模拟

在我们建立的旋转浅水实验系统上进行了可重复的系列模拟实验,成功地观测到大尺度持续存在的涡旋的产生、漂移与演化。在一定条件下,呈现出一个自持的、长寿命的、沿与整体旋转方向相反方向漂移的反气旋孤立波涡旋（Rossby soliton),这就是木星“大红斑”的实验室模型。     

关于反射直线和投影直线方程的一个注记

本文基于镜面反射矩阵理论,探讨了反射直线和投影直线方程更加简便的可行求法,且有着更加明显的几何意义,可一次性求解多条入射光线或多个反射面问题,在工程应用中更加方便．     

岩石复电阻率频散特性的机理研究

复电阻率测井是基于岩石频散特性发展起来的一种新的测井方法,目前对于复电阻率测井的岩石频散机理还没有一个统一的认识,通过理论和岩石频散实验数据的分析以及柯尔-柯尔模型对实验数据的拟合,初步明确了在小于10kHz的频率范围内,激发极化效应是引起岩石频散的主要因素,通过模拟井眼环境的岩石频散实验研究,验证了采用电极型电极系结构进行复电阻率测井的可行性．     

冲击接触问题的一种双共振投影梯度算法

根据冲击接触计算模型所需满足的基本控制方程和非线性互补条件,应用非线性互补问题与约束优化的等价关系将非线性互补接触问题转变成一个非线性规划问题,系统地推导建立了冲击接触问题的一种双共轭投影梯度计算方法．增广Lagrange乘子法克服了罚函数要求减小迭代步长以达到计算稳定的限制,即使对于冲击接触问题亦可以采用较大迭代步长,在形成的与原互补问题等价的无约束规划模式下,应用双共轭投影梯度算法提高非线性搜索速度和计算效率．算法模型计算结果表明,所建立的双共轭投影梯度计算理论及方法是正确有效的．     

Function Projective Synchronization of Two Identical New Hyperchaotic Systems

A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.     

Complex Wave Excitations in Generalized Broer-Kaup System

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.     

Entanglement in a generalized Jaynes--Cummings model

We investigate the pairwise entanglement and global entanglement in a generalized Jaynes--Cummings model, which can be used to realize Greenberger--Horne--Zeilinger (GHZ) entangled state (Zheng S B 2001 {\it Phys. Rev. Lett.} {\bf 87} 230404). Our results show that the W-type entangled states cannot be generated based on the model. The dependences of entanglement on Rabi frequency $\lambda$ and dipole--dipole coupling strength ${\it \Omega}$ are given. It is found that there exists the quantum phase transition when $\lambda={\it \Omega}$. For typical experimental data, the critical temperature for pairwise entanglement is on the order of $10^{-6}$\,K. Based on these results, two strategies that overcome decoherence are proposed.     

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Using the projective Riccati equation expansion (PREE) method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.     

投影寻踪和神经网络方法研究金属离子水解规律

对金属离子水解常数pK1的线性模型的局限性进行了讨论,并采用投影寻踪技术对pK1数据结构进行研究。非线性建模可能是更适宜的方法。采用函数连接型神经网络(FLN),以金属离子的电荷、半径、价电子结构、电负性及空价轨道数等作为描述变量,对60种金属离子水解常数pK1数据进行建模,获得了满意的结果,并对10种金属离子的pK1作出了预测。