淬火过程中具有非线性表面系数考虑相变时温度场的有限元分析

温度场的计算对淬火过程中热应力和热应变的分析有较大影响，对淬火后试件的残余应力和微观结构分析也有较大影响·本文以４２ＣｒＭｏ钢圆柱体试件为研究对象，从相变等温动力学ＴＴＴ图，给出了连续冷却相变动力学ＣＣＴ图的数学模拟计算式，计算了钢淬火过程中相变组织成分百分比，将热物性系数处理为温度和相变体积百分比的函数，用有限单元法计算了淬火过程中具有非线性表面系数考虑相变时的温度场·并建立了相应的泛函，为以后计算淬火的热应力和热应变做好准备工作     

Fluent模拟不同内部石蜡相变问题的典型模型分析

对相变传热问题的数学模型进行了简要介绍,分析了用Fluent软件模拟不同管道/容器内部石蜡相变问题的两种典型计算模型:等效热容法模型和焓法模型的特点与适用范围.最后结合典型计算模型介绍了目前用Fluent模拟不同管道/容器内部石蜡相变问题的研究现状.     

考虑旋转壳几何非线性时的随机响应研究

提出了一种统计线性化迭代法（IMSL）。利用这种方法,在形成非线性几何关系等效线性项的基础上,建立了非线性振动方程的等效刚度矩阵。通过求解方程,分析了几何非线性对旋转壳随机响应的影响。     

含湿相变粗糙多孔材质的热质耦合分形研究

多孔材质复杂的内部结构和含湿状态对传热和传质特性有着重要意义,其热质耦合传递过程广泛存在于能源开发和工程隔热等领域。不同于在多孔材质理想状态下对传热和传质特性的单方面分析,该文将孔道的分布参数、粗糙表面、含湿状态和相变等因素考虑进去,运用分形理论推导出了含湿相变粗糙表面多孔材质的渗流系数和耦合等效导热系数的表达式。结果表明,渗流系数与面积分形维数、含湿饱和度呈正相关,与相对粗糙度、迂曲分形维数呈负相关;耦合等效导热系数与渗流系数、相变量呈正相关,与相对粗糙度呈负相关。此外,结果还表明,相变量以及相变引起的气体膨胀压强差对热质耦合传递也有着重要影响。     

焊接过程瞬态温度场与残余应力场

本文根据焊接热传导及热弹塑性的研究现状,对如下两个问题进行了探讨.首先,采用非线性问题线性化的方法对非线性非定常温度场问题的边界元法做了改进,并将其用于焊接热传导分析:其次,提出“等放线膨胀系数法”考虑相变对于应力场的影响,并将其用于焊接热弹塑性分析.实例的数值计算结果与实测数据的对比分析表明本文方法行之有效.     

金属材料热处理过程中的瞬态温度场与解态相变的数值计算方法

本文首先将Kirchhoff变换推广到导热系数为温度的多项式的非定常非线性热传导问题.并用分析方法确定热传导问题的边界条件.其次提出以孕育期叠加法并引用线性混合法则来模拟金属热处理过程的多相瞬态相变,较为简便地确定相变的开始时间、相变的种类及相变组织的数量.最后利用三维双重边界元法分析工件多种形式的热处理全过程.算例的数值计算结果表明本文方法行之有效.     

高压气体淬火过程中的温度场与相变耦合问题的计算

高压气体淬火技术是一种现代的、有效的材料加工技术．在Cheng所得到的高压气体淬火过程中非线性表面换热系数的基础上,用有限单元法对钢淬火过程的温度场与相变耦合问题进行了模拟计算．在数值计算中,材料的热物性系数被处理为温度和相变体积百分比的函数．为避免数值解的震荡,采用了Norsette有理近似法．     

分析非线性系统随机响应的一种等效非线性化方法*

本文提出了分析非线性系统随机响应的一种新的等效非线性化方法。文中阐述了该方法的基本思想和处理方法,并对几种常见类型的非线性系统进行了分析和计算,结果表明,利用本文提出方法所得的均方位移响应与精确解或者Monte Carlc模拟解之间具有较好的一致性,并比等效线性化方法有更高的精度。     

发汗冷却系统的控制及其特性*

本文给出热层三维发汗冷却控制系统的数学模型.在一般情形下,它是一个可变域上分布参数和集中参数混合的非线性控制系统.本文指出:在冷却剂渗流是一维不可压缩的(或一维定常的)条件下,热层的传热和烧蚀问题可以单独求解.针对热防护层的表面烧蚀问题,本文讨论了系统控制方案,阐明简化的条件,研究了一维发汗冷却系统点控制的特性,给出了冷却剂无相变和有相变两种情形的平衡状态解.     

基于失效域重构和重要抽样法的结构动力学系统首穿失效概率

对于线性动力学系统，重构系统失效域，利用基本失效域概率构造重要抽样密度函数，提出了基于重要抽样技术的首穿失效概率估计方法；对于非线性动力学系统，构建等效线性系统，线性化原理为线性与非线性系统对安全域边界具有相同的平均上穿率.最后给出Gauss(高斯)白噪声激励的线性与非线性系统的数值算例，并与Monte-Carlo(蒙特 卡洛)方法及区域分解方法比较，结果显示该文方法是正确有效的.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.     

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) ＞ - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.     

CONTENTS OF VOLUME 30

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