Second-Oorder Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.     

一类离散非线性系统降维观测器设计

讨论了一类离散非线性系统降维观测器的存在性。对给定的Lyapunov函数,在保证观测误差渐近稳定的条件下,给出了该离散非线性系统降维观测器的设计方法。用数值例子说明了该设计方法的有效性。     

Nonlinear numerical simulation on extreme-wave kinematics

A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.     

Perturbed solution of sea-air oscillator for the E1 Ni(n)o/La Ni(n)a-Southern Oscillation mechanism

A class of coupled system of the E1 Ni(n)o/La Ni(n)a-Southern Oscillation (ENSO) mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for corresponding problem is considered.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

Wavelet analysis and nonparametric test for climate change in Tarim River Basin of Xinjiang during 1959–2006

Using wavelet analysis, regression analysis and the Mann-Kendall test, this paper analyzed time-series (1959–2006) weather data from 23 meteorological stations in an attempt to characterize the climate change in the Tarim River Basin of Xinjiang Uygur Autonomous Region, China. Major findings are as follows: 1) In the 48-year study period, average annual temperature, annual precipitation and average annual relative humidity all presented nonlinear trends. 2) At the 16-year time scale, all three climate indices unanimously showed a rather flat before 1964 and a detectable pickup thereafter. At the 8-year time scale, an S-shaped nonlinear and uprising trend was revealed with slight fluctuations in the entire process for all three indices. Incidentally, they all showed similar pattern of a slight increase before 1980 and a noticeable up-swing afterwards. The 4-year time scale provided a highly fluctuating pattern of periodical oscillations and spiral increases. 3) Average annual relative humidity presented a negative correlation with average annual temperature and a positive correlation with annual precipitation at each time scale, which revealed a close dynamic relationship among them at the confidence level of 0.001. 4) The Mann-Kendall test at the 0.05 confidence level demonstrated that the climate warming trend, as represented by the rising average annual temperature, was remarkable, but the climate wetting trend, as indicated by the rising annual precipitation and average annual relative humidity, was not obvious.     

基于非线性动力学模型的旅游生态容量分析

近年来,大量增加的游客给景区的旅游生态容量带来了较大的压力,矛盾日渐突出。为了实现景区的环境保护与可持续发展,研究游客活动量与景区旅游生态容量之间的关系是十分必要的。本文从非线性动力学观点出发,构建二者非线性动力学模型,并进行平衡态分析。研究结果表明:(1)系统要达到可持续发展,必须建立在景区环境的自我更新能力及人工恢复程度之和大于外界污染水平,且游客的增长率必须保持在较低水平的基础上;(2)景区旅游生态容量的承载力是有限的,所能容纳的游客也是有限的,超过一定的限度就会引起生态系统失衡。采取严格控制游客量,加强对景区内外环境的保护和改善、提升游客素养等措施,对于系统的协调发展至关重要。     

非线性Kuamoto-Sivashinsky方程的精确控制

运用泛函分析性质以及Fourier变换的方法研究带有周期边界条件的非线性k-s方程在有限时间区间上的精确控制.首先研究线性化k-s方程的精确控制,证明对于任意给定的函数u0∈Hs,uT∈Hs,总能找到一个控制函数h使得线性化k-s方程有解u且满足u(x,0)=u0,u(x,T)=uT;然后结合线性化k-s方程的精确控制,通过定义Fredholm算子并应用Fredholm算子的一些理论找到非线性化k-s方程的控制函数,使其可精确控制.     

改进的单纯形法及其在非线性参数估计中的应用

采用了改进的单纯形法,该算法利用遗传算法的变异操作来增强单纯形法的全局搜索能力,既兼顾了全局收敛性,又具有高效的局部搜索能力。并通过实例验证了该算法的优越性,以及应用于测量上的非线性最小二乘估计的可行性。     

地心坐标反解大地坐标的非线性方程组牛顿迭代法分析

目前的一些地心坐标向大地坐标的转换模型在计算速度,稳定性或精度方面存在一定的局限性。本文探讨了非线性方程组数值迭代的求解方法及其在MATLAB 7.0中的编程实现,并将结果与基于一元三次方程求解的严密方法做了比较分析,结果证明该方法是可以在实际中参考应用的。