Kirchhoff弹性杆动力学建模的分析力学方法

以杆的横截面为研究对象，讨论了其自由度，给出了截面虚位移定义，并定义变分和偏微分运算对独立坐标服从交换关系. 给出了曲面约束的基本假设，讨论了约束对截面自由度的影响以及加在虚位移上的限制方程. 从D'Alembert原理出发结合虚功原理，建立了弹性杆动力学的D'Alembert-Lagrange原理，当杆的材料服从线性本构关系时，化作Euler-Lagrange形式、Nielsen形式和Appell形式. 由此导出了Kirchhoff方程以及Lagrange方程、Nielsen方程和Appell方程，得到 关键词： 超细长弹性杆 分析力学方法 Kirchhoff动力学比拟 变分原理     

关于完全平方公式的几个猜想

归纳猜想是科学发现的最常用的方法之一 ,它具有很大的创造性 .本文应用归纳和类比的方法研究了完全平方公式 ,并得到了几个新的猜想 .     

A prediction of the acoustical properties of induction cookers based on an FVM–LES-acoustic analogy method

The FVM–LES-acoustic analogy method (FVM–LES-AAM), which is a hybrid prediction technique for the acoustical property computation, is presented and performed in this paper. The FVM–LES-AAM was developed by combining the finite volume method (FVM), the large eddy simulation (LES), and the Ffowcs Williams-Hawkings analogy algorithm (FWH-AA). To predict the acoustical properties of induction cookers, the FVM is used for discretizing the calculation field and building numerical equations, and the LES and FWH-AA are performed for computing the sound sources and predicting the far-field sound, respectively. Using the FVM with the unstructured grids method to discretize the control equation of Navier–Stokes was introduced for illuminating the above numerical simulation procedure. To prove the FVM–LES-AAM method is feasible for predicting the acoustical property of induction cookers, the simulated results were compared with some measured experimental data. The comparisons suggest that the hybrid method is accurate and reliable for the aeroacoustics analysis of induction cookers. Considering the temperature performance, furthermore, some new configurations for the noise reduction of induction cookers were designed, simulated, and discussed. The FVM–LES-AAM prediction technique shows promise as a feasible and computationally affordable approach for not only noise analysis of induction cookers, but also for other aeroacoustics problems in engineering.     

基于普朗特类比的多种强化管内污垢数据分析

针对光管和四种不同结构的强化管(缩放管I、缩放管Ⅱ、弧线管及波纹管)在相同条件(工质流速、入口温度、水浴温度及微粒浓度)下的颗粒污垢实验数据,基于普朗特类比法,以φ(φ=(Km/Kmp)/(f/fp),Km为质量传递系数,f为摩擦因子,下标p表示光管)和ψ(ψ=j/jp)/(f/fp)1/3,J为传热因子)作为传热性能...     

非逻辑创造思维在数学发现中的作用

借助实例介绍归纳法、类比法、联想以及减弱条件提出猜想这些非逻辑创造思维方法在一些重大数学发现中所发挥的作用.     

Myth,language, and complex ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical‐mathematical points of view. The following hypotheses are established: (1) language L is a self‐explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–81, 2014     

有机化学概念教学中类比的设计研究

类比思维作为一种高阶思维,在创新型人才的培养中起着重要作用。尽管这种高阶思维的培养难以量化评估并且在科学教育研究中缺乏明确的指导,但它却与类比教学的细节设计息息相关。因此,根据类比推理的结构映射理论,对有机化学概念中类比的课堂呈现进行了映射图解设计,注重引导学生关注关系结构,以期在有机化学教育的点滴渗透中加强学生对类比推理过程的了解,并促进其高阶思维的形成。     

First stereoselective total synthesis of helicascolides A and C

The first total synthesis of helicascolides A and C is reported via acid catalyzed acetonide deprotection followed by intramolecular lactonization in one-pot as the key step.     

Structural analogies on systems of deformable bodies coupled with non-linear layers

The paper is addressed at phenomenological mapping and mathematical analogies of oscillatory regimes in systems of coupled deformable bodies. Systems consist of coupled deformable bodies like plates, beams, belts or membranes that are connected through visco-elastic non-linear layer, modeled by continuously distributed elements of Kelvin–Voigt type with nonlinearity of third order. Using the mathematical analogies the similarities of structural models in systems of plates, beams, belts or membranes are obvious. The structural models consist by a set of two coupled non-homogenous partial non-linear differential equations. The problems to solve are divided into space and time domains by the classical Bernoulli–Fourier method. In the time domains the systems of coupled ordinary non-linear differential equations are completely analog for different systems of deformable bodies and are solved by using the Krilov–Bogolyubov–Mitropolskiy asymptotic method. This paper presents the beauty of mathematical analytical calculus which could be the same even for physically different systems.The mathematical numerical calculus is a powerful and useful tool for making the final conclusions between many input and output values. The conclusions about nonlinear phenomena in multi-body systems dynamics have been revealed from the particular example of double plate׳s system stationary and non-stationary oscillatory regimes.     

玻尔兹曼分布的计算机模拟

利用Lennard—Jonee,分子相互作用模型模拟气体分子在重力场中的分布,展现分子运动的过程和分布形态,说明重力场中分子分布由分子问频繁的碰撞所决定而与分子速率和位置的初态分布无关,。零势能”处的数密度no也并非常数,它不仅与分子质量m有关,而且还与温度T有关。此外,模拟也揭示了玻尔兹曼分布律是对大量粒子而言的统计规律。