正则化长波方程的三次样条差分模拟

本文对正则化长波方程(RLW方程)的时间、空间项分别采用三次样条公式进行离散,所得到的差分方程为三点、三层隐格式,对时间的精度为四阶,对空间的精度为二阶,每个时间步只需求解一个三对角方程组,而三次样条配置法在每个时间步中需要求解三个三对角方程组。本文对单个孤立波的演化进行了计算,参数与文[8]相同,其结果与解析解的最大绝对误差均保持在10~(-3)的量级以内,与文[8]给出的数值方法精度相当。对两、三个孤立波的相互碰撞,本文结果显示出在忽略10~(-3)量级的误差后,碰撞前后的孤立波形状保持不变,无论是一个孤立波的演化,还是两、三个孤立波相互碰撞,当将波形放大100倍后均可以发现有振荡的尾波,这说明这类振荡尾波的产生并非真实的物理现象,而是由数值误差产生的。本文认为仅从工程应用的意义上说,RLW方程具有孤立子性质的结论是可以接受的。     

泥沙起动条件及机理的非线性研究

 分析了单颗粒、均匀沙及非均匀沙的起动现象及其机理，认为泥沙的起动属于突变论研究的范畴。从泥沙起动所遵循起动条件的力学规律出发，导出泥沙起动条件方程。在此基础上，利用尖点突变性质对各种泥沙起动现象及机理进行了描述和说明。     

Optimal Operation of Reservoir Systems using Simulated Annealing

A stochastic search technique, simulated annealing (SA), is used to optimize the operation of multiple reservoirs. Seminal application of annealing technique in general to multi-period, multiple-reservoir systems, along with problem representation and selection of different parameter values used in the annealing algorithm for specific cases is discussed. The search technique is improved with the help of heuristic rules, problem-specific information and concepts from the field of evolutionary algorithms. The technique is tested for application to a benchmark problem of four-reservoir system previously solved using a linear programming formulation and its ability to replicate the global optimum solution is examined. The technique is also applied to a system of four hydropower generating reservoirs in Manitoba, Canada, to derive optimal operating rules. A limited version of this problem is solved using a mixed integer nonlinear programming and results are compared with those obtained using SA. A better objective function value is obtained using simulated annealing than the value from a mixed integer non-linear programming model developed for the same problem. Results obtained from these applications suggest that simulated annealing can be used for obtaining near-optimal solutions for multi-period reservoir operation problems that are computationally intractable.     

三峡水电站充水保压蜗壳平面非线性分析

采用自编的三维钢筋混凝土非线性有限元程序，对三峡水电站充水保压蜗壳进行了平面非线性分析，分析了钢蜗壳及外围钢筋混凝土的应力变形特性。非线性计算分析表明，在蜗壳进口断面处，虽然外围混凝土较薄，但在设计内水压力、结构自重和设备重量这些荷载组合作用下，蜗壳进口断面混凝土可能不会开裂，因此钢材应力均比较低，结构具有较高的安全度。说明现有配筋方案钢筋用量可能偏多，没有充分发挥钢材的作用，在进一步设计时可以适当优化。     

采用ZnO灭磁时阀片均流/均能的探讨

从ZnO电阻的非线性特性出发,对采用ZnO作为灭磁电阻时阀片的均流/均能进行理论论述,指出阀片均能性能的好坏主要依赖于阀片自身的特性;分析比较了ZnO阀片的不同选择方法对均流/均能的影响,指出阀片的均流/均能很大程度上取决于可供选择的阀片的库存量.该研究为发电机励磁系统的安全稳定运行提供了有力的保证.     

基于深度神经网络的高位滑坡范围预测

以贵州尖山营滑坡为工程背景,通过对深度学习的总结与分析,建立多层感知器模型以对该滑坡危险区范围进行非线性预测研究。通过对深度神经网络算法的优化,构建64-128-32-1四层多层感知器模型,并以滑坡最大高差、滑坡体积、滑源区坡度、坡脚坡度、地层倾角作为输入量,以滑坡最大水平运动距离作为输出量对该模型进行训练,实现影响因素与运动距离的非线性映射。根据对贵州省尖山营滑坡调查和研究,尖山营滑坡区域面积约648 700 m2,体积约1 200万 m3,属于特大型滑坡。依据最优模型对该滑坡进行滑距预测,滑坡平面直线距离1 769 m区域内为危险区域。     

我国股票市场的混沌探析

运用混沌理论对我国股票市场进行了实证研究 ,结果显示我国股票市场是一个低自由度的混沌系统 ,具有自相似的非线性结构 ,并且这种非线性结构可以用 GARCH( 1 ,1 )模型来拟合。     

论企业的非线性性质

企业作为一个系统,其关键特征是系统的非线性。我们以Adam Smith的大头针工厂作为简单的示例,从个体的生产函数推导出一个非简单加总的总体生产函数,从知识的角度不失一般性地解释了企业非线性性质的来源,并对已有的关于企业性质的论述做了简单的评论。     

Noisy chaotic dynamics in commodity markets

The nonlinear testing and modeling of economic and financial time series has increased substantially in recent years, enabling us to better understand market and price behavior, risk and the formation of expectations. Such tests have also been applied to commodity market behavior, providing evidence of heteroskedasticity, chaos, long memory, cyclicity, etc. The present evaluation of futures price behavior confirms that the resulting price movements can be random, suggesting noisy chaotic behavior. Prices could thus follow a mean process that is dynamic chaotic, coupled with a variance that follows a GARCH process. Our conclusion is that models of this type could be constructed to assist in forecasting prices in the short run but not over long run time periods.First version received: June 2001/Final version received: March 2003