On the evolution of applied mathematics

The recent trend in the application of mathematics to biological sciences is discussed in historical perspective. It is suggested that this new development should be regarded as a natural evolution of applied mathematics in the expansion of its scope. The mathematical concepts and methods to be used are not expected to be substantially different from those used in traditional applied mathematics. For illustration, we sketch an application of the kinetic theory of the study of dissipative systems to the study of the structure and function of protein molecules. The traditional concepts and methods of statistical physics can be successfully applied to yield predictions for comparison with empirical data. The Chinese edition of this paper will be published in Advances in Mechanics (in Chinese), 2003, 33(2): 161–165     

应用力学方法初探

应用力学在二十世纪初期，大放异彩，大获成功。力学在解决现代工程问题的过程中，创造性地发展了一套行之有效的应用力学方法。本文对应用力学在中国的传播与发展、有关应用力学的论述、应用力学方法的范例、应用力学方法的意义与特点、以及应用力学与数学力学、应用力学与有限元法之间的联系等方面作了介绍和讨论。阐明了应用力学方法必然产生的实际背景和理论根源。并指出：深刻探究与理解应用力学的范例是学习与掌握应用力学方法的有效途径。     

麦克斯韦对应用力学的贡献

麦克斯韦不但在经典物理学上具有崇高的地位,而且对应用力学的发展也做出了巨大贡献.他在应用力学方面的研究涉及到弹性力学、光弹性、结构力学、黏弹性力学、天体力学、流体力学、动力稳定性等方面. 在研究应用力学的过程中,他将娴熟的数学技巧和对物理本质的准确把握有机地结合在一起,其研究方法与后人所提倡的技术科学和应用数学的学术思想是相通的.     

Applied Problems in the Mechanics of Strain Hardening of Structural Metallic Materials

Some applied problems of the mechanics of strain-hardening processes in metallic materials are considered. To solve these problems, the concept of loading surface, which separates the elastic and elastoplastic domains in the stress space, is used. Strain-hardening models are analyzed. For a wide range of steels and alloys, the most commonly used hypothesis of isotropic-and-kinematic hardening is experimentally justified __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 12–51, October 2005.     

Mathematics of Philosophy or Philosophy of Mathematics?

This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics.     

外加极化电位对316L不锈钢微动磨蚀行为的影响

采用球－平面接触微动磨损试验机考察了轧制固溶316L不锈钢在不同极化状态下的微动磨蚀行为。结果表明：在阳极极化状态下,随着极化电位的升高,腐蚀疲劳微断裂作用增强,促进了微动损伤过程的发展;在阴极保护状态下,摩擦系数随微动过程的变化规律及微动损伤形貌与阳极极化态下的存在显著差异,在阴极极化态下,微动磨擦副之间的粘着导致较高的微动摩擦应力状态,但与阳极极化态相比并未产生严重损伤。     

应用数学的拓展——用一篇关于蛋白质分子的结构和功能的动理论发展的论文来说明

近来,人们喜欢从历史的角度来探讨数学在生物学中的应用问题.这种趋势似乎可以看作是应用数学范围逐渐拓展的一种自然现象.但它所用到的数学概念和方法与以往应用数学所用的概念和方法并无本质区别.例如,我们在本文中简单描述了如何将耗散系统中的动理学原理用于研究蛋白质分子的结构和功能.在这些研究中,传统统计物理学的概念和方法可以用来成功地建立与经验数据相对应的假设及理论.      

外加电场对边界润滑条件下钢—钢摩擦副摩擦磨损性能的影响

利用球－盘式摩擦磨损试验机,考察了钢－钢（ＳＵＪ２／Ｓ４５Ｃ）摩擦副在不同润滑剂润滑下的摩擦磨损性能及外加电场对摩擦磨损性能的影响。结果表明：施加电压,特别是改变电压极性可使摩擦副的摩擦磨损性能发生很大变化,而电场及其极性对摩擦磨损性能的影响效果取决于润滑剂及边界润滑膜的性质。     

热弹流润滑椭圆接触区内表面凹陷现象的研究

通过理论分析和光干涉实验 ,考察了纯滑动热弹流润滑椭圆接触区内当卷吸速度与接触椭圆短轴成 0°和 45°角时出现的油膜局部增厚现象 ,即固体表面在接触区出现凹陷的现象 .解释了玻璃盘 -钢滚子接触副表面凹陷的形成原因 ,揭示了凹陷的深度、位置和形状随卷吸速度及接触椭圆短轴夹角的变化规律 .     

求解转子系统突加不平衡响应方法的研究

本文提出并研究了用传递函数分析法求转子系统的突加不平衡响应,讨论了求这一响应的最佳数值积分方法。用本文提出的理论解方法及三种常用的数值积分法:尤拉后差法,纽马克法,及呼伯特法,对一模型转子算例进行了分析计算,结果表明;尤拉后差法最适用于求转子系统的突加不平衡响应。本文提出的传递函数分析法,可以和试验模态分析方法相结合,以求解复杂转子系统的突加不平衡响应。     

In Memory of Our Honorary Editor-in-Chief Editorial Board of Applied Mathematics and Mechanics

Chien Wei-zang,one of the founders of modern mechanics in China,a world renowned scientist,educator,outstanding social leader,prominent leader of the Chinese Democratic League and a close friend of the Communist Party of China,the Vice Chairman of the 6th,7th,8th,and 9th National Committee of Chinese People's Political Consultative Conference, the Vice Chairman of the 5th, 6th, and 7th Central Committee of Chinese Democratic League, the Honorary Chairman of the 7th, 8th, and 9th Central Committee of Chinese Democratic League, a senior member of Chinese Academy of Science, the President of Shanghai University, the Director of Shanghai Institute of Applied Mathematics and Mechanics, and the Honorary Editor-in Chief of Applied Mathematics and Mechanics, Passed away at the age of 98 in Shanghai at 6:20 AM on July 30,2010.     

非线性转子-轴承系统涡动的机械化数学分析

为研究转子一轴承系统中非线性油膜力引起的半速涡动，本文给出了将吴文俊消去法和符号计算相结合的分析方法。基于短轴承假设，得到了单盘转子系统涡动时盘心、轴心及涡动角速度相对于无量纲转速的关系式。分析研究了转子涡动角速度变化规律及出现的双稳态现象。     

引入温-粘及压-粘关系式的油膜工作性能数值分析

为了研究温-粘及压-粘效应对液体静压支承系统中油膜工作性能的影响,本文以大尺寸液体静压支承转台为研究对象,建立了三维立体油腔模型,采用有限体积法,模拟计算了引入温-粘及压-粘关系式时,油腔内部流体的承载力及温升变化情况.计算结果表明,温-粘特性及压-粘特性在很大程度上影响油腔内的承载能力和湿升.引入了温-粘及压-粘关系...     

考虑损伤拉压不同模量梁的纯弯曲

根据考虑损伤的变模量弹性理论,建立了考虑损伤的拉压不同模量梁的弯曲基本方程,推导了梁的拉（压)应力、受拉区高度和挠度的计算公式．应用数值计算方法,分别得到了有损与无损时梁极限拉（压）应力、受拉区高度与模量比的关系曲线以及有损梁的最大挠度和模量比的关系曲线,同时得到了梁拉（压）应力比值、损伤引起的中性轴偏移量和梁跨中挠度比值与载荷的关系曲线．这些结论可为工程上具拉压不同模量梁的截面设计提供一定的参考价值．     

Approximate estimation of hardening-softening behaviour of circular pipes subjected to pure bending

An approximate method for describing the plastic hardeningsoftening behaviour of circular pipes subjected to pure bending is presented. Theoretical estimation based on the uniform ovalization model and local collapse model proposed in the paper is incorporated to give several simple formulations with reasonable accuracy for determining the relationship between bending moment (M) and curvature (k) in the purely bended pipes. Attention is focused on the critical curvature associated with maximum resistant moment and the maximum change in the original diameter before the end of uniform ovalization stage as well as the local collapse behaviour. Some comparisons between analytical results and experimental results are made in order to examine the theory.     

Finite element modified method of characteristics for the Navier–Stokes equations

An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection–diffusion, Burgers and unsteady incompressible Navier–Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier–Stokes equations, an approach that can be conceived as a fractional step method is used. The innovative first stage of our method is a backward search and interpolation at the foot of the characteristics, which we identify as the convective step. In this particular work, this step is followed by a conjugate gradient solution of the remaining Stokes problem. Numerical results are presented for:

• a Convection–diffusion equation. Gaussian hill in a uniform rotating field.
• b Burgers equations with viscosity.
• c Navier–Stokes solution of lid‐driven cavity flow at relatively high Reynolds numbers.
• d Navier–Stokes solution of flow around a circular cylinder at Re=100.

Copyright © 2000 John Wiley & Sons, Ltd.     

温度效应对覆冰导线舞动特征的影响研究

以某耐张段单跨导线作为研究对象,基于哈密顿原理和增量热场理论,建立了考虑温度效应的覆冰导线非线性舞动模型并推导出其舞动方程。分别使用近似模态和复杂模态得到离散后的面内-面外耦合的有限维度舞动方程,接着采用多尺度法得到该方程的近似解。数值算例研究表明,温度对频率的影响与Irvine参数有关,对张力的影响与初始张力的范围有关,而且降温会增大导线舞动幅值;采用精确模态计算得到的舞动幅值显著小于使用近似模态计算得到的幅值。     

On the Potential of Tomographic Methods when Applied to Compacted Crushed Rock Salt

Compacted crushed rock salt is considered as potential backfill material in repositories for nuclear waste. To evaluate the sealing properties of this material knowledge concerning the nature of the pore space is of eminent interest. Here, the pore microstructures of crushed rock salt samples with different compaction states were investigated by X-ray (XCT) computed tomography and Focused Ion Beam nanotomography (FIB-nt). Based on these methods the pore microstructures were reconstructed and quantitatively analyzed with respect to porosity, connectivity and percolation properties. Regarding pores with radii \(> 4\,\upmu \hbox {m}\) , porosity differs substantially in the two analyzed samples ( \(\phi = 0.01\) and 0.10). The pore microstructures are considered isotropic in connectivity and percolation threshold. Using two finite-scaling schemes we found percolation thresholds with critical porosities \(\phi _{c} > 0.05\) . Based on statistical considerations, the millimeter size samples that can be analyzed by XCT are large enough to provide a meaningful picture of the pore geometry related to macroporosity. The samples contain also a small fraction (i.e. \(< 0.01\) ) of pores with radii \(< 1\,\upmu \hbox {m}\) , which were resolved by FIB-nt. Often these pores can be found along grain boundaries. These pores are granular shaped and are not connected to each other. Typical samples size that can be analyzed by FIB-nt is on the order of tens of microns, which turned out to be too small to provide representative geometric information unless an effort is made that involves several FIB-nt realizations per sample.