粘性流体理论中一类奇异非线性边界值问题

该文研究了起源于粘性流体理论中的一类奇异非线性边界值问题，利用摄动法技巧，确立了问题正解的存在性和唯一性的充分条件．     

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case,the homotopy analysis method (HAM) is used. to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu's model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.     

具有热源项的驻点流动和传热问题的近似解析解

研究持续拉伸变形表面上二维平面和轴对称驻点流的动量和热量传输问题。利用同伦分析方法获得速度分布和温度分布的级数解,讨论了级数的敛散性。通过图形分析主流速度与拉伸速度的比率参数,普朗特参数,热源参数和流动类型指标对速度边界层和温度边界层的影响。结果表明,这些参数对二维平面驻点流动和传热有较大的影响。     

基于研究型教学理念的数学建模和最优化课程建设

针对数学模型与最优化课程的特点和要求,设计培养大学生创新能力的研究型教学模式:教学内容的设计坚持四个原则、教学过程重在启发与互动、课内外学习重在研究、数学软件的应用重在与课程整合等.通过各个环节提高学习的主动性,激发学习兴趣,培养学生应用数学解决实际问题的能力,进一步推动创新人才的培养.经过两轮教学实践表明:本课程的教学设计合理、教学效果良好,值得尝试.     

微极性流体在上下正交移动的渗透平行圆盘间的流动

分析了上下正交运动的两平行圆盘间的非稳态的不可压缩的二维微极性流体的流动．应用von Krmn类型的一个相似变换,偏微分方程组(PDEs)被转化成一组耦合的非线性常微分方程(ODEs)．应用同伦分析方法,得到方程的解析解,并且详细讨论了不同的物理参数,像膨胀率,渗透Reynolds数等,对流体的速度场的影响．     

边界耦合的Marangoni对流边界层问题的近似解析解

研究了由温度梯度引起的Marangoni对流边界层问题.由于动量方程和能量方程的边界条件耦合,利用相似变换将偏微分方程组转化为常微分方程非线性边界值问题.通过巧妙引入摄动小参数对速度和温度边界层方程同时渐近展开求解,得到了问题的近似解析解,并对相应的动量、能量传递特性进行了讨论. 关键词： Marangoni对流 近似解析解 渐近展开     

两相复合材料有效热导率的理论推导

复合材料有效热导率的解析表达式一直是传热问题中人们想要解决的问题.本文选用合适的单元体,采用热阻模型和积分平均方法,分别对分散相为球体和圆柱体的两相复合材料的有效热导率进行了推导.对于多孔复合材料,当孔隙率较大或温度较高时辐射换热的影响不能忽略,本文分析了气孔为球体或圆柱体时辐射换热对其有效热导率的影响.将计算所得有效热导率与相关实验数据进行了比较,结果表明两者吻合较好,证明了公式的准确性.     

疫情背景下微积分“课程思政”的教学探索与实践

结合当前的疫情,采用画龙点睛式、隐性渗透式等教学方式,多角度、全方位把“思政”元素融入到微积分教学之中,通过调查问卷评估了课程思政教学效果,为高校微积分课程的“课程思政”改革提供一种思路.     

Diffusion dynamics in branched spherical structure

Diffusion on a spherical surface with trapping is a common phenomenon in cell biology and porous systems. In this paper, we study the diffusion dynamics in a branched spherical structure and explore the influence of the geometry of the structure on the diffusion process. The process is a spherical movement that occurs only for a fixed radius and is interspersed with a radial motion inward and outward the sphere. Two scenarios govern the transport process in the spherical cavity: free diffusion and diffusion under external velocity. The diffusion dynamics is described by using the concepts of probability density function (PDF) and mean square displacement (MSD) by Fokker-Planck equation in a spherical coordinate system. The effects of dead ends, sphere curvature, and velocity on PDF and MSD are analyzed numerically in detail. We find a transient non-Gaussian distribution and sub-diffusion regime governing the angular dynamics. The results show that the diffusion dynamics strengthens as the curvature of the spherical surface increases and an external force is exerted in the same direction of the motion.     

高等数学教学中如何培养学生创新能力的实践

课堂教学是对学生进行教育的主要方式,教师在教学活动中应该始终注意根据教学内容创设能激起学生新异感的问题情景,引导学生从一个问题出发,联想、分析、思辨,沿着各种不同的途径去思考,去发现多种关联问题及寻求解决方法.本文作为文[7]的姊妹篇,从众所熟知的积分中值定理教学谈起,阐述教师如何在课堂教学中引导学生由某个问题出发去联想一系列相关问题,使学生的数学思维不断攀升,培养学生科学思维方法和创新能力.