The octahedral algorithm,a new simplicial fixed point algorithm

A new variable dimension simplicial algorithm for the computation of solutions of systems of nonlinear equations or the computation of fixed points is presented. It uses the restrart technique of Merrill to improve the accuracy of the solution. The algorithm is shown to converge quadratically under certain conditions. The algorithm should be efficient and relatively easy to implement.Partially supported by the Western Michigan University Sabbatical and Faculty Research Funds.     

Reporting computational experiments in mathematical programming

This paper presents a set of recommended standards for the presentation of computational experiments in mathematical programming.The authors are members of the Committee on Algorithms of the Mathematical Programming Society.     

Analytical inverse solution for coupled thermoelastic problem for the evaluation of contact stress during steel strip rolling

Knowledge of the contact stress between roll and strip is a critical factor in modern, high-speed rolling mills. Previously two inverse analytical methods have been developed to determine the elastic contact stress on the one hand and the heat flux or the temperature in the whole roll (and especially at the surface) on the other hand, by measuring the stress tensor inside the roll body with fibre optics and by measuring the temperature with a thermocouple fully embedded at only one point inside the roll. However measurements done by fibre optics take into account the elastic stress and the thermal stress. However the contact stress was determined under isothermal assumption, which is strongly incorrect for hot rolling conditions. In this paper, the coupled thermoelastic problem is solved analytically using the theorem of superposition and the expression of the temperature field exhibited previously. A significant improvement of the accuracy of the inverse method for reconstructing the contact stress is observed by taking into account thermal stress. Hot rolling simulation is given to demonstrate this result. The computation time is studied to rapidly optimise the industrial parameters during the rolling process, and considering that both inverse methods have been run, the computation of thermal stress does not cost significant additional CPU times.     

Computation of certain infinite series of the form for arbitrary real-valued k

We provide a general method from which one may obtain more arbitrary closed form solutions for infinite series of the form ∑f(n)n^k, for and sufficiently well-behaved f(n). We illustrate the methods for the special case of f(n)=aⁿ/n!, obtaining generalizations to the Bell numbers and polynomials.     

Sur les approximations « isotrope » et « anisotrope » de l''opérateur tangent pour les méthodes tangentes incrémentale et affineOn the ‘isotropic’ and ‘anisotropic’ approximations of the tangent operator in the incremental tangent and affine methods

Three localisation rules, TFA, the incremental tangent, and the affine method, are recalled and evaluated in the context of the elastoplastic micromechanical analysis of heterogeneous materials, composites or polycrystals. With the help of a severe example, it is shown how methods based on the complete anisotropic elastoplastic tangent operator yield very stiff predictions which are far from the reference solution; the same conclusion holds for the method using the elastic accommodation rule. On the other hand, using an isotropic form of the tangent operator delivers much better responses. The reasons for such differences are discussed, together with possible justifications for the choice of the isotropic form. To cite this article: J.-L. Chaboche, P. Kanouté, C. R. Mecanique 331 (2003).     

Finding all solutions to polynomial systems and other systems of equations

In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the solution paths from each of the trivial solutions into the solutions of the given system. All solutions to the given system were thereby obtained.This paper utilizes a different approach that eliminates the requirement of the previous paper for a leading dominating term in each equation. We add a dominating term artificially and then fade it. Also we rely on mathematically more fundamental concepts from differential topology. These advancements permit the calculation of all solutions to arbitrary polynomials and to various other systems ofn equations inn complex variables. In addition, information on the number of solutions can be obtained without calculation.Work supported in part by NSF Grant No. MCS77-15509 and ARO Grant No. DAAG-29-78-G-0160.Work supported in part by ARO Grant No. DAAG-29-78-G-0160     

用FLUENT软件计算化学氧碘激光流场

用计算流体动力学(CFD)软件FLUENT,数值研究化学氧碘激光喷管形线,碘喷孔位置, 副流入口压力, O2(1Δ)初始产额,水蒸汽含量以及稀释气体对平均小信号增益系数沿流动方向分布的影响;并对大连化学物理研究所超音速化学氧碘激光的两次实验进行数值模拟,计算结果显示平均小信号增益系数与实验测试的摩尔功率趋势一致。     

SSPH核近似的降元算法研究

本文首先介绍传统光滑粒子流体动力学（Smoothed Particle Hydrodynamics,简称SPH）方法的基本公式,用对称（Symmetric）光滑粒子流体动力学（SSPH）核近似方法函数.函数一阶导数和函数二阶导数的计算进行了研究,在SSPH方法的基础上提出了精度较高、计算量少和所占内存空间较低的降元算法.对SSPH核近似方法和降元算法的精度进行了分析,SSPH方法和本文提出算法用于一维函数的一阶导数和二阶导数的计算,并进行误差对比分析发现精度有所提高.最后本算法应用于非稳态热传导问题上,同时进行数值计算和对比分析,验证了本方法的有效性.     

碳1s电子能量的理论计算及在ESCA中的应用

用 X射线光电子能谱测定碳材料中碳 1s电子的结合能 ,是分析碳材料中碳原子有机结构的方法之一。本文利用量子化学从头计算程序对碳 1s电子的能量进行理论计算 ,结果表明 ,理论计算值与 ESCA仪器提供的标准值具有非常好的相关关系 ,用等式可表示为 :仪器推荐结合能 =(1.0 72± 0 .0 0 2 )×计算结合能。根据这一关系式 ,利用实验所得的元素组成 ,确定可能形成的化合物结构用量子化程序进行了理论计算 ,从而实现对未知结构碳材料样品 ESCA谱图的解析