竞争不可逆化学反应过程工艺特征数学模型的解析

数学模型可用来研究化工工艺的稳定性和多样性,入口工艺参数的不同组合及出口状态等工艺特征.探索获取指定选择率入口工艺参数的不同组合及范围并证明入口工艺参数组合的多种工艺出口状态(参数).通过数学模型图解的方法能得到出口状态全解,给出完整的工艺稳定体系特征图包括各种出口状态的转变,工艺过程的各种不稳定状态.用数学模型图解详细分析伴有竞争不可逆化学反应的反应精馏工艺多种分离状态并存的原因及其与工艺参数的依存关系,定性讨论分离状态稳定性情况,分析用分离状态极值边界数学模型作工艺设备费用和操作费用之间经济核算的可行性.     

铸件凝固过程数值模拟

本文建立了东方汽轮机厂生产的20万瓩汽轮机高压缸内缸铸件危险截面凝固过程的数学模型,并编制了相应的软件,能在 IBMXT/AT 机上显示出危险截面凝固的动态过程和缩松缩孔的大小及位置.计算结果与实物“解剖”吻合得很好.本软件还能通过改变工艺条件,利用计算机进行反复试浇并显示,为工艺人员寻求最佳工艺方案提供了方便.     

化学反应生成物浓度预测、控制数学模型的研究

根据化学动力学理论,由化学反应速率的定义,利用机理分析法以及反应速率微分方程,对化学反应的生成物浓度与时间、温度的关系进行了定性、定量分析.根据不同的反应条件,深入研究并建立及推广了生成物浓度数学模型.经实验检验,建立的数学模型具有高度的概括性、准确性,可应用于预测、控制化学反应系统、优化工艺过程.     

线性不对称损失时非正态分布过程均值优化

针对常见的两种非正态分布———梯形分布和三角分布，研究线性不对称质量损失时其过程均值的优化问题，建立了梯形分布在五种不同情况下线性不对称质量损失的数学模型，基于以上模型给出了线性不对称质量损失时梯形分布最优过程均值的确定方法；研究三角分布在四种不同情况下线性不对称质量损失的数学模型，并给出了线性不对称质量损失时三角分布最优过程均值的确定方法。最后，用实例验证本过程均值优化模型的有效性。实例表明，应用线性不对称损失函数，适当的改变过程均值，可以有效地降低产品的质量损失，通过调整工艺过程将获得最佳经济效益。     

基于无敏感性调查模型中数学模型建立的实验技术研究

本文系统阐述了在建立无敏感性调查模型中,数学模型建立的指导思想和基本程序.详细介绍了在建立数学模型的过程中,组织实验调查的方法、步骤和技术要求.给出了数学模型的建立过程及其一般形式.     

回归正交试验设计在水飞蓟素提取工艺中的应用

本文针对水飞蓟素提取工艺利用二次回归正交设计 ,进行了五个变量的正交回归设计 ,获得了最佳的试验工艺参数值以及相应的数学模型     

电测深确定最佳井位的数学模型及其应用

在电测深确定最佳井位过程中 ,本文运用模糊数学和灰色关联度理论建立确定最佳井位的数学模型 ,并通过实例验证了该数学模型的科学性和实用性     

试论数学建模在初中数学教学中的应用

数学模型就是根据研究目的,对所研究的过程和现象的主要特征、主要关系,采用形式化的数学语言,概括地、近似地表达出来的一种结构,即把所要研究的实际问题,通过数学抽象构造出相应的数学模型,再通过数学模型的研究使原问题获得解决的过程.在目前的初中数学教学中,经常要用数学建摸来解答问题 使用数学建模方法的步骤和要求是: 1.建立数学模型 数学模型要反映现实原型的本质特征和主要关系;要加以合理的简化;要有严密的逻辑结构,以利于推理和获得真实的结论.     

电化工艺中的自由边界问题

本文考虑了二个电化工艺中的自由边界问题:电加工问题和电镀问题,简要地介绍了这二个问题的数学模型和已经取得的理论成果。     

惯性往复振动设备的机电耦合模型和瞬态过程分析

采用建立离散系统动力学方程的矩阵法,建立了双旋转偏重激振的惯性往复振动设备的动力学方程,该动力学方程与两驱动电机的状态方程一起构成了惯性往复振动设备机电耦合的数学模型．通过分别对不同阻尼、不同电机功率时数学模型的数值仿真和对仿真结果分析,揭示了惯性振动设备瞬态过程的实质,提出了减小振动体瞬态振幅和缩短瞬态过程的新方法．为该类设备瞬态过程的智能控制和工程设计提供了可靠的数学模型．     

Dynamics and Coarsening of Interfaces for the Viscous Cahn—Hilliard Equation in One Spatial Dimension

In one spatial dimension, the metastable dynamics and coarsening process of an n -layer pattern of internal layers is studied for the Cahn–Hilliard equation, the viscous Cahn–Hilliard equation, and the constrained Allen–Cahn equation. These models from the continuum theory of phase transitions provide a caricature of the physical process of the phase separation of a binary alloy. A homotopy parameter is used to encapsulate these three phase separation models into one parameter-dependent model. By studying a differential-algebraic system of ordinary differential equations describing the locations of the internal layers for a metastable pattern for this parameter-dependent model, we are able to provide detailed comparisons between the internal layer dynamics for the three models. Layer collapse events are studied in detail, and the analytical theory is supplemented by numerical results showing the different behaviors for the different models. Finally, an asymptotic-numerical algorithm, based on our asymptotic information of layer collapse events and the conservation of mass condition, is devised to characterize the entire coarsening process for each of these models. Numerical realizations of this algorithm are shown.     

Methods of statistical modeling in the process of sieve separation of heterogeneous particles

In the article we undertook the attempt of using the theory of random fields in the analysis of the separation process of particles in non-contiguous systems. The presentation of the complete model is a complicated problem. We can say that this article is start point of the theory, which will be supplemented gradually in the future. The separation process of particles on sieves is a phenomenon with random character. It is a result of random character of cleaned mixture and the nature of the separation process. Undoubtedly, an important part is played by the theory of random fields in which system-events, inherently not determined, are described in undetermined-probabilistic way. However, we can perceive one paradox in such actions – correctly constructed probabilistic models serve to impose deterministic frames on the given random process. We can say that stochastic models generate the matrix of the causal-consecutive dependence, which will give the ability of controlling a given process.     

Towards an Automated Reduction Method for Polynomial ODE Models of Biochemical Reaction Systems

This paper presents the first version of an algorithmic scheme dedicated to the model reduction problem, in the context of polynomial ODE models derived from generalized chemical reaction systems. This scheme, which relies on computer algebra, is implemented within a new MAPLE package. It is applied over an example. The qualitative analysis of the reduced model is afterwards completely carried out, proving the practical relevance of our methods. We would like to thank Marc Lefranc and Pierre-Emmanuel Morant. This work was partially supported by the PPF Bioinfo of the University Lille I.     

脑内各向异性扩散传质与吸附反应过程数值分析

对脑组织内传质过程的机理及其影响因素进行了分析,建立了综合考虑脑内物质各向异性扩散、吸附和反应过程的数学模型,模型方程采用隐式控制容积法进行数值求解.计算结果表明:组织迂曲度越大,物质的扩散越慢,当某一方向迂曲度较小时,物质浓度明显增大,物质扩散变快,由于脑组织的非均质性,脑内物质的扩散传递存在着竞争现象;吸附与反应作用会抑制脑内物质传递,吸附速率越大,抑制现象越明显,对于脑内非线性的米氏反应过程,当反应速率常数增大时,稳定浓度会显著减小,同时米氏常数的增大则会使得稳定浓度值增大.相较于吸附过程,米氏过程的抑制性作用更为明显.     

Fast Reaction Limit with Nonmonotone Reaction Function

We analyse the fast reaction limit in the reaction-diffusion system with nonmonotone reaction function and one nondiffusing component. As speed of reaction tends to infinity, the concentration of the nondiffusing component exhibits fast oscillations. We identify precisely its Young measure which, as a by-product, proves strong convergence of the diffusing component, a result that is not obvious from a priori estimates. Our work is based on an analysis of regularization for forward-backward parabolic equations by Plotnikov. We rewrite his ideas in terms of kinetic functions which clarifies the method, brings new insights, relaxes assumptions on model functions, and provides a weak formulation for the evolution of the Young measure. © 2022 Wiley Periodicals LLC.     

Time/depth dependent diffusion and chemical reaction model of chloride transportation in concrete

This study focuses on the physical and chemical processes that control the transport of chloride ions into concrete structures. An analytical solution of a diffusion reaction model is presented for determining the time/depth dependent chloride diffusivities considering both diffusion process and binding mechanism of chloride occur simultaneously. The diffusion-reaction model, which is based on the Fick’s second law of diffusion and a mathematical formulation for an irreversible first-order chemical reaction, is used to precisely describe the diffusion mechanism of chloride diffusion process. When the chemical reaction is considered, the free chloride concentration is slowly reduced since some of the free chloride ions have reacted with cement paste such that the diffusion coefficient is also reduced simultaneously. The diffusion-reaction model predicts a longer service life than the total and free chloride diffusion models that do not consider the effect of the chemical reaction during the chloride diffusion process.     

基于合作博弈的买方抗衡势力市场绩效与卖方工艺创新强度分析

设计了由一个上游企业和两个下游企业所构成的产业链纵向关系模型,建立了纵向一体化、纵向分离且下游企业均无买方抗衡势力、以及单个下游企业具有买方抗衡势力三种情况下上游企业的工艺创新强度计算模型,分析了下游企业存在买方抗衡势力时市场中均衡的批发价格、零售价格、企业利润以及社会福利的变化,给出了相应的结论,同时也说明了“加尔布雷斯假说”在本文的结构下没有得到验证。     

Memory effects and random walks in reaction-transport systems

In this article, we study continuous and discrete models to describe reaction transport systems with memory and long range interaction. In these models the transport process is described by a non-Brownian random walk model and the memory is induced by a waiting time distribution of the gamma type. Numerical results illustrating the behavior of the solution of discrete models are also included.