日本核污染对我国扩散影响预测

本文针对核污染扩散问题,建立了对放射性粉尘在空气中传播方向和浓度变化的模型.首先根据质量守恒定律导出无风条件下放射性物质的扩散,然后在扩散模型中应用风速方向上的浓度时间函数,得到改进的扩散模型.模型中考虑到风场影响下的放射性物质扩散规律,采用对流扩散模型,引入时间分数阶偏微分方程,进而通过已知数据分析放射性尘埃对其扩散趋势做出预测.     

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.     

数码照相颜色数值与物质浓度辨识的数学模型

在一定的环境条件下,可以认为一种物质溶液的浓度确定了该溶液的颜色,因此可以根据溶液的颜色来判断物质溶液的浓度.根据观测数据,应用SPSS软件对二氧化硫的浓度和数码照片颜色RGB读数进行了相关性分析.在此基础上建立了二氧化硫溶液浓度与颜色的RGB读数的多元二次多项式回归模型,并用MATLAB软件对模型求解.进一步地,还深刻分析了RGB变量对物质浓度的判断的交叉影响,并建立了完全的二次多项式模型.最后在残差分析的基础上,引入相对残差的概念对所得模型进行了误差分析.结果显示,完全二次多项式回归模型具有更高的相关系数和更小的残差方差,并且所得到的模型非常简洁.     

空气中PM2.5问题的研究

主要研究空气污染中的PM2.5扩散问题.首先利用相关分析法讨论了PM2.5与SO_2,NO_2,CO,PM10,O_3的相关性,建立线性回归方程;然后建立一维的反应扩散方程,预测PM2.5浓度变化,并定量与定性分析西安市空气污染状况;再建立高斯烟羽模型,对持续高浓度PM2.5扩散情形进行拟合,并对污染物扩散范围进行预测,得到重度污染以及可能安全区域;最后通过建立最优化模型,得到较有经济效益的空气治理方案.     

空间生态学中的一些反应扩散方程模型

本文旨在介绍反应扩散方程模型在生物学中的应用,重点考虑空间非均匀环境对种群动力学、物种进化和疾病传播的影响.一方面通过建立并分析一系列反应扩散方程模型,把空间生态学、物种进化和疾病传播这些方面有机融合起来,试图了解各种生物过程以及机制.另一方面通过建立新的数学模型、提出新的数学问题、发展一些新的数学方法,促进反应扩散方程基础理论的发展.讨论内容包括非均匀空间中的单个物种数量、非均匀环境对竞争物种的影响、扩散和移流在物种生存和竞争中的作用、非均匀环境中的物种进化、单个或多个浮游植物的生存和竞争、河流中的物种扩散、非均匀空间中的疾病传播和变异等问题.     

含孔隙混凝土二维细观建模方法研究

根据混凝土的细观组成和结构特点,对传统二维建模方法加以继承与改进,提出了一种高效的分步入侵判定算法.将孔隙直观地反映在模型中,建立了不同的含孔隙混凝土细观模型.对含圆形、椭圆形、多边形骨料与圆形、椭圆形孔隙的混凝土标准试件分别进行了建模研究,结果表明本文的算法具有较强适用性.同时,通过对不同面积率与多种形状骨料/孔隙混凝土的大量建模进一步验证了该算法的效率.模拟了混凝土试件在单轴压缩下的准静态力学性能,分析了混凝土内部孔隙对其裂纹扩展的主要路径、破坏模式以及宏观力学性能的显著影响.     

镁离子内扩散铌酸锂单晶光纤的研究

利用镁离子内扩散铌酸锂单晶光纤,实现了晶纤具有芯-包层波导结构,得到了包层晶纤的损耗比扩镁前晶纤损耗降低约14倍的好结果,并对镁离子内扩散机理、晶格发生畸变的原因等进行了分析和讨论.通过X射线衍射分析和扫描电子显微镜观察扩镁表面,发现在表面富镁层有一新化合物结构,可能是Li-Mg-Nb-O组成的三元系相结构,并提出和实验证实这一富镁层的新化合物是镁离子内扩散铌酸锂晶纤的真正扩散源.     

混凝土中氯离子扩散的二次有限元分析

大量研究表明,氯离子在混凝土中的扩散严重影响了混凝土的耐久性.基于Fick第二定律,考虑二维扩散问题,采用灵活度较好的三角形剖分单元和精确度更高的二次插值基函数,建立了氯离子在混凝土中扩散的二次有限元模型,并进行了收敛性分析.同时,对常数边界、线性边界、振荡边界的二次有限元模型进行数值模拟,有效地预测了氯离子在三种边界条件下的扩散趋势.     

微通道中电渗流及微混合的离子浓度效应

电渗流广泛应用于微流控芯片中的流体输运与混合.该文提出了一种离子浓度梯度对电渗流及微混合产生影响的变量模型,采用有限元分析方法对微通道中电渗流及微混合的离子浓度效应进行了数值模拟,分别讨论了zeta电势、介电常数等对微通道内流场和浓度场的影响规律,定量分析了微混合效率.结果表明,当zeta电势和介电常数随浓度变化时,微通道中流场分布不均匀,离子分布不对称.当溶液浓度趋近1 mol/L时,溶液基本无法进入微通道.微混合效率随溶液间浓度差的增大而减小,而且浓度差越大越能在较短距离内到达充分混合.     

含时滞的反应扩散方程组周期解的存在与稳定性

本文研究了一类反应项非单调的时滞反应扩散方程组.利用上、下解方法及不动点理论获得了此系统边值问题周期解存在性的充分条件,给出了证明其周期解稳定性的方法.最后通过化学中的一个典型模型说明了所得结果的意义.     

Model for cover cracking due to corrosion expansion and uniform stresses at infinity

The mechanical model of the cover layer cracking in reinforced concrete structures due to corrosion expansion of reinforcement and uniform stress at infinity is established in this paper. The principle of superposition and the series expansion technique of the theory of complex potential established by Muskhelishvili are applied. The complex stress potentials are assumed to be in the form of Taylor and Laurent series expansions, and the unknown coefficients are determined by the boundary conditions and the stress state at infinity. Finally the analytical solution for hoop stresses in concrete is derived. Referring to the previous studies in the literature, the equation for time of concrete cracking due to corrosion expansion of reinforcement and uniform stresses at infinity is established. It is found that the change of stress state at infinity may accelerate or decelerate the initiation of crack. In addition, compared with the case without corrosion, the existence of corrosion products can alter the location of cracking. Further analyses indicate that the effect of the ratio between reinforced bar and concrete on the cracking is insignificant, and that the possibility of cover layer cracking increases with increasing penetration of corrosion.     

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.     

Mathematical model of the pipeline with angular joint of elements

A mathematical model of the pipeline as a Koiter-Vlasov moment shell with kink lines of the surface at the junctions of the pipe segments was constructed and substantiated. The following tasks are solved: The geometric parameters of the mechanical system as a three-dimensional elastic body and as a shell are found; force factors of the shell are expressed in terms of displacements of the middle surface of the wall, taking into account the presence of a kink line; equations of pipe equilibrium are derived as Koiter-Vlasov shells with an edge along the line; forces on oblique sections are expressed as functions of shell movements; the conjugation conditions on the pipe joint line for displacements and the angle of rotation of the normal are imposed and justified; conjugation conditions for bending moments, shear forces, transverse and normal forces are imposed and justified. The presence of the solution singularity at points on the connection line of the pipe segments is theoretically established and illustrated by the numerical example.     

The Analysis of Model on Population Growth with Stage-structure in the Polluted Environment

In this paper,the authors considered a single-species model with stage-structure in a pollutedecological environment.Subject to the outside toxin input quantity being stable,the authors established thesufficient conditions under which the species will be permanent using Lyapunov method.At the same timebiological implications briefly of these results are discussed.     

Bi-nonlinear vibration model of tubing string in oil & gas well and its experimental verification

Fluid-induced vibration (FIV) prediction is an important prerequisite work in wear and fatigue analysis of tubing string in oil & gas well. The finite element method, energy method and Hamiltonian principle are comprehensively used to establish a single nonlinear vibration model of pipe conveying fluid, taking into account the longitudinal/lateral coupled vibration. Based on the contact/impact theory of elastic/plastic body, the nonlinear contact-impact model of tubing-casing is established and introduced into the single nonlinear vibration model to form a bi-nonlinear vibration model of tubing string in oil & gas well. The bi-nonlinear model is numerically discretized by the finite element method, solved by Newmark− β method, and verified preliminarily by a classical contact/impact example in literature in which the influence of inflow is not taken into account temporarily. A similar experiment of tubing vibration is designed and completed to further test the validity of the bi-nonlinear vibration model by comparing the frequency-domain and time-domain responses of the experiment with those from the model. The analysis shows that the bi-nonlinear model has good calculation accuracy and the vibration response law is basically consistent with the experimental results, which can provide an effective theoretical analysis tool for FIV behavior of tubing string in oil & gas well.     

Exact solutions of potentiostatic current transients for a corrosion reaction under mixed charge transfer and diffusion control

An analytical solution has been obtained for the current response transients to a potentiostatic step for a corrosion reaction where a planar metal electrode is immersed in an acidic electrolyte. This solution can be used to provide values of important kinetic parameters of the reaction such as corrosion current and Tafel slopes. The model is derived for conditions of mixed charge transfer and diffusion control and includes the metal ion deposition partial reaction. A Nernstian diffusion model is used, where anodic and cathodic species diffuse in a finite diffusive layer. A numerical solution has previously been published [1], but it is believed that this is the first time an analytical solution has been presented. Transients obtained by including both the metal dissolution and metal-ion deposition (back) reactions, are compared to those obtained by neglecting the metalion deposition reaction. It is shown that neglecting the back reaction can cause significant errors especially when large cathodic potential steps are applied and as the corrosion current approaches the limiting current density of the cathodic reaction.     

纯增益反馈控制律在MF模型中的应用研究

给出蒙代尔-弗莱明模型的动态表述,并证明蒙代尔-弗莱明模型的动态系统具有能控性、能达性、能观性等结构特征.在蒙代尔-弗莱明模型动态系统的基础上对开放经济条件下宏观经济模型的供需均衡问题转化为宏观经济政策的控制律设计问题,得出开放经济条件下宏观经济政策的纯增益反馈控制律的解析解并且对控制律的解析解的政策含义作出阐述.本文...     

Prediction of the penetrated rust into the microcracks of concrete caused by reinforcement corrosion

Consider a steel-rust-concrete composite consisting of a circular cylindrical concrete cover and a coaxial uniformly corroding steel reinforcement. Prediction of the amount of rust penetrated into the microcracks of concrete cover from a set of data measured at the surface of the concrete is of particular interest. The steel is assumed to be linear isotropic and rust follows a power law stress–strain relation. For the concrete, anisotropic behavior and post-cracking softening model is employed. The formulations lead to a nonlinear boundary value problem which is solved analytically. A key parameter β, defined as the ratio of the volume of corrosion products inside the cracks to the volume of the cracks, is calculated. With some efforts, this parameter is also extracted from the available theoretical and experimental studies for the purpose of comparison. The effects of the mechanical properties of rust and concrete on β is addressed.     

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.     

反映混凝土单边效应的弹塑性损伤本构模型及应用

为了尽可能有效和准确地描述混凝土材料的非线性力学特性,在研究国内外混凝土损伤本构模型的基础上,基于连续介质损伤力学和不可逆热力学的理论框架,采用统一强度理论作为屈服破坏准则,分别定义拉、压双标量损伤来考虑材料的拉、压迥异特性,同时引入反向加载影响因子以修正拉压交替循环加载时材料的单边效应,以及多轴应力状态下拉、压损伤累积的相互影响,最终采用显式积分算法建立了一种改进的混凝土弹塑性损伤本构模型.不同素混凝土加载试验模拟结果初步验证了建议模型的有效性,而通过对含I型裂缝的混凝土简支梁试验进行数值分析,结果表明,所得的荷载 挠度曲线与试验结果吻合良好,进一步检验了模型应用于结构非线性分析的有效性.