“接触式轮廓仪的自动标注”的问题解析

就2020年"高教社杯"全国大学生数学建模竞赛D题"接触式轮廓仪的自动标注"给出了一种求解方法,并针对学生在参赛论文中出现的问题作了简要的说明与点评.为保证求解的连贯性,论文的前一部分是问题的求解,后一部分是参赛论文的点评.     

机载平台式惯导系统导电环故障机理分析及解决措施

导电环是平台式惯导系统惯性平台的重要组成部分,主要承担惯性平台台体内各种信号与系统的传输和交联,导电环发生故障直接会导致惯导系统失效。针对导电环三种故障模式:接触电阻变大、绝缘强度降低以及烧坏,本文采用微动磨损和电接触理论,结合作者的实际工作经验,对故障机理进行了分析,提出了相应的改进措施。这些措施均在生产中得到落实。落实措施后的故障统计表明,采取的改进措施有效,导电环的故障率与原来相比降低了38%。     

Interpretation of vicinal proton–proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors

The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling of the dynamic behavior of systems with rolling elements

Bearings, friction wheels, cams, etc. are widely employed elements in machine construction. The modeling of the dynamics of rolling friction plays therefore a crucial role in the simulation and optimization of such systems. This paper describes a recently developed transient-rolling-friction model with its application to different generic dynamical systems, to simulate the effects of rolling friction or traction on the dynamics of mechanical systems. The results, which are expressed in terms of the complex stiffness arising in the rolling-contact patches, show that the behavior depends on both the amplitude and the frequency of oscillation. For low amplitudes and frequencies, the behavior is quasi-linear. For increasing amplitudes and frequencies, however, strong non-linearities appear, leading to complex behavior.     

Hodge numbers of nodal double octics

Let B be a surface of even degree d in P³ with nodes as the only singular points. In [1] Clemens proved that the topology of the small resolution of the double covering of P³ branched along B depends not only on the number of nodes but also on the so-called defect, a non-negative integer describing their configuration.

The aim of this note is to give an elementary proof of the Clemens. result and to present some geometric interpretation of defect.     

The boundary element method applied to elastic contact problems with friction

In the current paper the boundary integral equations (BIE) for elastic contact problems with friction are derived from the incremental virtual work principle. After introducing contact conditions of adhesion and slip into BIE all variants on boundary are made to discretize by quadratic isoparametric boundary element. In the current paper not only an auto-increment loading law is presented but also the iterative calculation laws for open, slip and adhesion condition are given. The results of numerical examples are satisfactory.     

带摩擦的弹性接触问题广义变分不等原理的简化证明

在弹性摩擦接触问题中 ,从变分原理出发来研究接触问题 ,可以将摩擦力纳入问题的能量泛函 .为了得到摩擦约束弹性接触问题的能量泛函 ,日前大多是用拉格朗日乘子法 ,但拉格朗日方法用在变分不等问题中 ,要利用非线性泛函分析和凸分析来证明 ,证明复杂 .本文利用向量分析的工具及巧妙的变换 ,对带摩擦约束的弹性接触问题的广义变分不等原理进行了严格的证明 ,由于只用到向量分析 ,简化了证明 .     

Theory for electron hopping through nanometer-scale contacts: From tunneling regime to ballistic regime

Using the recursion-transfer-matrix (RTM) method combined with nonequilibrium Green's function (NEGF) method, we study the electronic states and current–voltage (I–V) characteristics of junction systems with atomic-scale nanocontacts as a function of the distance between electrodes. We observe a strong nonlinear behavior in the I–V characteristics and correspondingly a gap structure appears in conductance. We find that such a nonlinear behavior emerges when the transport properties change from tunneling to ballistic regimes.     

On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation

This paper is concerned with properties of the wave speed for the stochastically perturbed Fisher–Kolmogorov–Petrovsky–Piscunov (FKPP) equation. It was shown in the classical 1937 paper by Kolmogorov, Petrovsky and Piscunov that the large time behavior of the solution to the FKPP equation with Heaviside initial data is a travelling wave. In a seminal 1995 paper Mueller and Sowers proved that this also holds for a stochastically perturbed FKPP equation. The wave speed depends on the strength σ of the noise. In this paper bounds on the asymptotic behavior of the wave speed c(σ) as σ→0 and σ→∞ are obtained.     

Fluorinated comblike homopolymers: The effect of spacer lengths on surface properties

A series of polyacrylate monomers with F‐alkylalkyl [F(CF₂)_n(CH₂)_n′] side groups were prepared by free‐radical polymerization. The effect of the chemical structure on the surface properties of poly(ethylene terephthalate)s was evaluated by variations in the relative length of the fluorocarbon and hydrocarbon units in the side group. The resulting polymers were quite surface‐active in the solid state. The surface and bulk organization was investigated by X‐ray photoelectron spectroscopy analysis. A strong correlation between the bulk organization and surface properties of the polymers was established. The outmost layer, formed from trifluoromethyl groups and some ester functions, suggests that the side chain is arranged irregularly in the polymer–air interface. The length of the lateral chain governs this organization: long fluorinated chains and short hydrocarbon spacers are essential elements of the molecular design for such low‐surface‐energy materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3737–3747, 2005