任意多边形匀面重心的计算方法

我们都知道 ,当一闭曲线所围几何图形Ω是一均匀薄片时 ,其重心计算公式是ｘ0 =1Ｍ Ωｘｄｘｄｙｙ0 =1Ｍ Ωｙｄｘｄｙ其中Ｍ= Ωｄｘｄｙ为薄片质量(设密度为 1 )但在作具体计算时我们都清楚 ,计算的难度完全取决于Ω的形状 ,而即使是像多边形这样的简单图形 ,当边数稍稍多一点 .运算量就颇大 .本文的目的在于寻找一种计算任意多边形(凸凹不限 )均匀薄片重心的方法 .为叙述方便 ,后文我们把多边形围成的均匀薄片的重心简称为多边形匀面重心 .定理 1　设Ω1 ,Ω2 ,… ,Ωｎ是对均匀薄片Ω的一个几何剖分 ,每个Ωｉ的面积记为Ｓｉ,∑ｎｉ=1…     

综合评判法在炼钢工艺研究中的应用

1 引言在我国的中小转炉中推广顶底复合吹技术对发展我国炼钢生产意义重大。为确定某15吨转炉复吹炼钢供气方案,曾在其他工艺参数大体相似条件下进行141炉次的复吹炼钢试验,分七种底部供气方案进行,其底吹供气强度及第一次倒炉取样前一分钟内的平均枪高列于表1。     

求解二维Poisson方程的重心有理插值配点法

首先介绍了重心Lagrange插值法,然后通过改变重心Lagrange插值法的插值权函数,重点给出了重心有理插值的具体形式.基于等距节点和Chebyshev节点这两类插值节点,利用重心有理插值配点法求解了二维Poisson方程,并比较了采用上述两种插值节点时的计算精度.数值算例表明,重心有理插值配点法具有稳定性好,计算精度高和程序编写简单的特点.     

重心法去模糊的环境舒适性指标评价

环境舒适性向来都是比较模糊的概念,对于人体来说只是感官上的瞬间感觉,难以用精确的数学描述,而且主观性较强.考虑到常规的去模糊评价方法容易忽略较小权重因素的影响,导致信息"丢失"的情况,从环境舒适性角度出发,提出重心法去模糊的综合评价方法.方法引用力学中重心的概念,刻画各个环境因素隶属度的集中程度,解决了去模糊过程中出现结果模糊的问题.分析实施例表明,重心法去模糊综合评价方法的分析结果与调查的实际情况较为吻合,吻合度约为91.4%,说明评价方法更具合理性和有效性,为后续的环境舒适性控制器提供准确的输入参量.     

有限差分-配点法求解二维Burgers方程

将重心插值配点法结合Crank-Nicolson差分格式来求解Burgers方程.首先,利用Hopf-Cole变换将Burgers方程转化为线性热传导方程;空间方向采用重心插值配点法进行离散,时间方向采用Crank-Nicolson格式离散,导出对应的线性代数方程组,并对此计算格式进行相容性分析;最后,通过数值算例验证此计算格式具有高精度和有效性.     

求解Helmholtz方程的无网格重心插值配点法

本文针对Helmholtz方程,借助Chebyshev插值节点,运用重心Lagrange插值基函数和重心有理插值基函数推导了求解该类方程的两种无网格配点法.首先,将插值基函数应用于空间变量及其偏导数,建立了基于配点法的二阶微分方程组.其次,在给定的插值节点上,利用微分矩阵对其进行了简化.最后通过三种测试节点来计算数值算例,从而验证了本文方法不仅可以计算大波数问题,还可以计算变波数问题,并且算法具有精确稳定、计算量小和高效等优点.     

求解二维Poisson方程的重心插值配点法

采用重心Lagrange插值配点法计算了二维Poisson方程.采用重心Lagrange插值法构造近似函数,由配点法离散Poisson方程及其边界条件.数值算例表明方法具有理论简单、计算精度高的特点.     

高速公路宏观社会经济影响定量评价方法研究

高速公路投入运营对社会经济发展的促进作用,不仅是验证高速公路决策正确与否的重要依据,而且为今后高速公路建设项目决策提供了重要依据.从定量分析角度出发,分析社会经济发展指数与经济指标、交通指标间的关系,建立了高速公路社会经济影响贡献模型,计算高速公路对社会经济发展的贡献值.然后,在贡献值的基础上提出贡献率的概念及其计算方法,并利用贡献值及贡献率综合确定高速公路对社会经济发展的影响程度.最后,以宜州至柳州高速公路为例,应用上述方法进行了实例计算.     

微下拉法YAG晶体生长数值模拟

对微下拉法生长YAG晶体进行包括感应加热在内的全局数值模拟,其耦合了感应加热、气体与熔体对流以及固液气三相的热输运,熔体对流同时考虑浮力与表面张力作用.为统一使用有限体积法离散控制方程,采用复函数法求解电磁场,与流函数法对比验证程序正确性.分析整个生长炉内的温度和流场(包括气体和熔体)分布,并针对固液交界面区域温度梯度较小的情况,改进后热器材料,为微下拉法晶体生长炉结构设计提供参考.     

扩散炉炉丝设计原理

电热管式扩散炉在半导体工业中是常用的。本文利用乘子法和脉冲变分原理讨论了扩散炉的炉丝设计问题，给出了设计原理和计算方法。     

多目标决策中的力学思想及其交互重心移动法

利用力学中的重心概念 ,提出求多目标规划问题满意解的交互重心移动法 .它不仅简便易行 ,而且可以有效地利用以前的信息 ,防止决策者前后判断不一致情况的出现 .     

Experimental Investigation of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments have been carried out to investigate the reorientation behavior of a free liquid surface in a partly filled right circular cylinder upon step reduction in gravity. In the initial situation the system is dominated by hydrostatic forces. In this case the equilibrium of the free liquid surface is generally characterized by a flat shape with a curvature at the cylinder wall given by the static contact angle. After transition to reduced gravity, capillary forces govern the flow and a capillary driven reorientation of the liquid to the new equilibrium position is established in a damped oscillation. The particular interest of this study is to determine the main characteristics of the surface oscillation as well as the behavior of the dynamic contact angle.     

Thin liquid droplet on top of a rotating non-isothermal liquid layer

Wafers are usually coated by using spin-coating, where centrifugal forces are used to spread a droplet on the rotating wafer. This flow is unstable to the fingering instability, where several segments of the wetting front spread faster than the average, resulting in several fingers. The liquid flows via the existing fingers while the area in between does not get coated. A precise experimental investigation is problematic, as the droplet has to be placed quite exactly in the center of the rotation. Replacing the wafer by a second liquid should lead to a parabolic-shaped free interface and the droplet should center itself due to gravity. Here, we derive a model for the free interfaces of a thin droplet on top of a rotating liquid by taking gravity, centrifugal forces, friction, (thermo-)capillary and line forces into account. Additionally, this setup is the simplest example of multiple coating, where several free interfaces and contact lines influence each other. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

“三焦点”广义椭圆曲线及其传导特性

提出了三焦点广义椭圆的概念,给出了三焦点广义椭圆的画法及其轨迹方程,建立了三焦点广义椭圆的重心M到三焦点广义椭圆轨迹曲线上动点P的距离d的数学模型,研究了三焦点广义椭圆构件对力与速度的传动特性及其在工业上的应用.     

圆型限制性三体问题中双恒星系统的存在性

在圆型限制性三体问题的研究中，研究较多的是在其中一体附近的运动。本文研究远离两个大质量恒星的行星的运行情况，在此范围内，使用KAM理论研究大振幅轨道的存在性，说明了星系中双恒星系统的存在性，而这一现象已被天文学家所观察到。     

Damping Behavior of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments were carried out to investigate the damping behavior of the reorientation of a free liquid interface in a right circular cylinder, partly filled with a liquid and suddenly exposed to a step reduction in gravity. The damping behavior basically depends on the Ohnesorge number and the static contact angle. This study shows the strong influence of the contact point for low static contact angles.     

陀螺仪运动的混沌与KAM理论

本文建立了外环轴水平放置的重力对称陀螺仪的运动方程．将非自由陀螺仪转子的质心位置作为扰动，利用Ｍｅｌｎｉｋｏｖ方法和ＫＡＭ理论研究了陀螺仪的运动，研究结果表明：在 螺仪转子的质心与支架中心不重合且充分接近时，或 螺仪能量充分大时，陀螺仪运动的Ｐｏｉｎｃａｒｅ映射既出现Ｓｍａｌｅ马蹄意义下的混沌，又存在ＫＡＭ不变环面和不变闭曲线。     

Modeling and control of surface gravity waves in a model of a copper converter

Undesirable splashing appears in copper converters when air is injected into the molten matte to trigger the conversion process. We consider here a cylindrical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid dynamics in a transversal section of the converter is modeled by a 2-D inviscid potential flow involving a gravity wave equation with local damping on the liquid surface. Once the model is established, using a finite element method, the corresponding natural frequencies and normal modes are numerically computed in the absence of injection, and the solution of the system with injection is obtained using the spectrum. If a finite number of modes is considered, this approximation leads to a system of ordinary differential equations where the input is represented by the fluid injection. The dynamics is simulated as perturbations around a constant fluid injection solution, which is the desired operating state of the system, considering that the conversion process does not have to be stopped or seriously affected by the control. The solution is naturally unstable without control and the resulting increase of amplitude of the surface waves are assimilable to the splashing inside the converter. We show numerically that a variable flow around the operating injection is able to sensibly reduce these waves. This control is obtained by a LQG feedback law by measuring the elevation of the free surface at the point corresponding to the opposite extreme to where the nozzle injection is placed.     

Tracking a near-field moving target using fuzzy neural networks

In this paper we explore the problem of tracking a near-field moving target using fuzzy neural networks (FNNs). The moving target radiates narrow band waves that impinge on an array of passive sensors. At a particular time instance, the location of the target is estimated by several judiciously constructed FNN-based angle and distance estimators. When the target is moving, its trajectory can be on-line estimated due to the parallel and real-time computational capability of the FNNs. Computer simulation results illustrate the performance of the FNN-based angle estimator, distance estimator, and the near-field moving target tracker.     

改进的云重心评判法在高技术企业信用评价中的应用

提出一种改进的云重心评判法,并应用于高技术企业信用评价.首先,借鉴TOPSIS法的基本思想,基于理想状态和负理想状态,对综合云重心向量进行归一化,并采用修正的加权偏离度来衡量云重心的变化,从而克服了传统云重心评判法的不足.其次,针对高技术企业信用评价中的不确定性,运用改进的云重心评判法对高技术企业信用状态进行实证测评,结果证明了该方法的合理性和适用性.