数学建模竞赛的发展与数学建模教师的作用

本文简要回顾数学建模竞赛活动的起源和发展,介绍国内外特别是国外学者关于提高数学建模教学质量的主要观点,并结合作者自身的经验和体会,探讨教师在数学建模教学中的作用。     

A self-similar solution to the equation of gas filtration in a spherically symmetric porous medium

We consider the Cauchy problem for the Boussinesq equation which describes filtration of a gas in a spherically symmetric porous medium. For the self-similar solution to this problem we construct a formal in the neighborhood of the point r → ∞ expansion and a convergent near r = 0 one.     

数学模型的本质定义和非常建模法

本文给出了融合现有数学模型定义的本质定义 ,提出了新的数学建模方法——非常建模法 .     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Mathematical modeling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines based on a thermodynamic multi zone model

The main purpose of the current study is mathematical modelling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines. A validated multi-zone model coupled to a semi-detailed chemical kinetics is used to predict homogeneous charge compression ignition combustion and emissions. Heat and Mass transfer submodels are linked to the multi-zone model. Bulk flow and diffusion mass transfer between zones are considered. The results indicate that the diffusion mass transfer is negligible in homogeneous charge compression ignition engines. Bulk flow mass transfer plays a critical role in homogeneous charge compression ignition simulation and applying it in the multi-zone model leads to accurate prediction of the start of combustion, peak pressure and exhaust emissions. The results show that the maximum error changes from 90% to 5% in carbon monoxide prediction and from 98% to 14% in unburned hydrocarbons prediction, using the mass transfer submodel.     

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

We study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a $2D$ porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of not-necessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional elliptic cell problem.The reaction–diffusion system describes the macroscopic diffusion, aggregation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of this two-scale problem relies on a suitable application of Schauder’s fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.     

慢速饮酒血液中酒精含量的数学模型

描述的是在一定时间内慢慢地匀速喝完一定数量酒的问题,并建立了相应的数学模型.同时也建立了快速饮酒的数学模型,以及证明了在各次饮酒后的某时刻酒精含量的可叠加性.     

Mathematical analysis of a model describing the number of antibiotic resistant bacteria in a polluted river

In France, 90% of surface water suffer from antibiotic pollution that increases the number of antibiotic resistant bacteria. The first indicator of water quality is revealed by the fish quality. According to the Le Conseil Supérieur de la Pêche, only 15% of rivers in France are considered in good condition, whereas 22% are in very bad condition. The bacterial resistance to antibiotics is a public health problem as it affects humans through drinking water; the treatment of water is costly. Mathematical modeling may estimate and predict the quantity of bacteria in rivers. In this paper, we investigate properties of the mathematical model estimating the number of bacteria in a river presented by Lawrence, Mummert and Somerville. Global analysis of equilibria is presented, using a Lyapunov function. Moreover, the existence of positive periodic solutions is proven. Copyright © 2013 John Wiley & Sons, Ltd.     

Mathematical modeling of angular distortions in laser ranging of the <Emphasis Type="Italic">RadioAstron</Emphasis> satellite

A mathematical model for angular distortions in satellite laser ranging is constructed with allowance for effects of the theory of general relativity. For the RadioAstron mission satellite, it is shown that the angular distortions exceed the present-day accuracy of angular measurements in satellite laser ranging at all orbit points. Manifested most strikingly in the neighborhood of apogee, these distortions have to be taken into account in data processing performed within the framework of high-accuracy space exploration programs.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

电厂冷却水在湖泊和水库中热扩散过程的数学模拟

本文对电厂冷却水排入湖泊和水库后的热扩散过程进行了数学模拟,建立了三维扩散方程,给出了一维、二维和三维计算湖泊和水库中任意点任意时刻水温上升量的计算公式,并通过实例对一维情形的计算公式进行了验证,结果很好.     

高校数学公共课教材质量定量比较评价模型

首先建立了评价高校数学公共课教材质量的指标体系 ,依据该指标体系 ,运用层次分析法 ,构建了对高校数学公共课教材质量进行定量比较评价的模型 .最后给出了应用实例 ,介绍了具体的评价分析方法 .     

The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age

The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal, and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years.