大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象.关键词：浅水波方程大尺度正压大气解析解非线性波     

缝洞型油藏溶洞内底水锥进现象的可视化研究

设计与建立了研究大尺度溶洞内近井地带油水两相流动特性的可视化实验系统,通过摄像机记录了水锥从形成到突破油层的过程,研究了水锥产生的机理和演变特性,同时得到了水锥高度与油层厚度随流量的变化关系。实验结果表明:水锥形成初期,油水界面存在轻微波动;水锥变化过程中,出现锥顶凹陷;底水突破油层时,锥顶处油水存在轻微混合;水锥高度与油层厚度变化率随流量的增大而增加。     

A High-Order Accurate Algorithm for Electrostatics of Overlapping Disks

A fast and accurate algorithm for the computation of effective electric and mathematically equivalent properties of composites with nonsmooth interfaces is reported. The algorithm is based on an integral equation reformulation of the electrostatic partial differential equation and a fast hierarchical technique for potential field evaluation. In a numerical example, 200 large and strongly inhomogeneous aggregates of randomly overlapping disks are solved with a relative error of 0.0005.     

Mathematical programming and electricity markets

The electric power industry in Europe and all over the world is undertaking major regulatory and operational changes. The underlying rationale behind all these changes is to move from a centralized operation approach to a competitive one. That is, the understanding of power supply as a public service is being replaced by the notion that a competitive market is a more appropriate framework to supply reliable and cheap electric energy to consumers. In some cases, the aforementioned transition process has included the privatization of power utilities. This new framework requires new tools and procedures, and some of these procedures drastically differ from traditional ones. Therefore, new challenging mathematical programming and operations research problems naturally arise in this context. This paper provides a review of some of these problems, particularly operational problems spanning a time horizon from one day to one year. The approach adopted emphasizes mathematical programming issues, describing the structure and characteristics of these problems and suggesting appropriate solution techniques. Relevant comments and suggestions were provided by Alexis Motto from McGill University, Montréal, Québec, Canada.     

Efficient Management of Multiple Sets to Extract Complex Structures from Mathematical Programs

Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the algebraic formulation is usually sufficient to retrieve different block structures from mathematical programs. These structured problems can then be solved by adequate solution techniques. To illustrate this idea we focus on stochastic programming problems with recourse. Taking into account both time and uncertainty dimensions of these problems, we are able to retrieve different customized structures in their constraint matrices. We applied the Structure Exploiting Tool to retrieve the structure from models built with the GAMS modeling language. The underlying mathematical programs are solved with the decomposition algorithm that applies interior point methods. The optimization algorithm is run in a sequential and in a parallel computing environment.     

A Log-Barrier method with Benders decomposition for solving two-stage stochastic linear programs

An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time. Received: August 1998 / Accepted: August 2000?Published online April 12, 2001     

四种无约束优化算法的比较研究

从数值试验的角度 ,通过对 3个测试问题 (其中构造了一个规模大小可变的算例 )的求解 ,对共轭梯度法、BFGS拟牛顿法、DFP拟牛顿法和截断牛顿法进行比较研究 ,根据测试结果的分析 ,显示截断牛顿法在求解大规模优化问题时具有优势 ,从而为大规模寻优算法的研究提供了有益的借鉴 .     

Decomposition method of descent for minimizing the sum of convex nonsmooth functions

This paper presents a descent method for minimizing a sum of possibly nonsmooth convex functions. Search directions are found by solving subproblems obtained by replacing all but one of the component functions with their polyhedral approximations and adding a quadratic term. The algorithm is globally convergent and terminates when the objective function happens to be polyhedral. It yields a new decomposition method for solving large-scale linear programs with dual block-angular structure.Supported by Program CPBP 02.15.The author thanks the two referees for their helpful suggestions.