污染物在非饱和带内运移的流固耦合数学模型及其渐近解

污染物在非饱和带中运移过程是多组分多相渗流问题.在考虑气相的存在对水相影响的前提下,基于流固耦合力学理论,建立了污染物在非饱和带内运移的流固耦合数学模型.对该强非线性数学模型采用摄动法及积分变换法进行拟解析求解,得出了解析表达式.对非饱和带内的孔隙压力分布、孔隙水流速以及污染物的浓度在耦合与非耦合气相条件下的分布规律进行解析计算.对该渐近解与Faust模型的计算结果进行了对比分析,结果表明:该模型解与Faust解基本吻合,且气相作用以及介质的变形对溶质的输运过程产生较大的影响,从而验证了解析表达式的正确性和实用性.这为定量化预报预测污染物在非饱和带中迁移转化和实验室确定压力-饱和度-渗透率三者之间的关系提供了可靠的理论依据.     

堆浸浸出率灰色动态GDM(1,1)预测研究

基于灰色系统理论扩展了GM(1,1)模型建模方法.给出了一些既改善原始数据列的光滑度,又减少还原误差的变换函数构造条件.首次将灰色动态模型结合变换函数应用于堆浸过程浸出率的预测.结果表明:该方法预测精度高,为实现浸出动力学未来行为的预测和控制提供了一种新的方法.     

对称的e1-球分布:性质与应用

本文研究了—个有用的n维e1-球分布族LSn和对称的e1-球分布的某些重要的性质.导出了z (z∈LSn)的边际分布、条件分布、生存函数、双边指数分布的尺度混合分布类(被表示为LSn,∞),讨论了它们的独立性、刻画和稳健性.并应用在非参数预测和数论网的产生中.最后,在模型诊断与异常值检验中,用蒙特卡罗方法,获得了非常有用的某些检验统计量的分位数.     

堆浸工艺水动力学研究

利用无量纲的形式推导出堆浸工艺中通过非饱和堆我动区和滞留区的溶质运移模型,通过最小二乘法确定模型参数,并就两种不同供液情形下的解析解进行了讨论.该模型可用来研究堆浸中溶质浓度的变化规律.     

各向异性液体-多孔饱和介质在机械荷载作用下的弹性动力分析

将一个各向异性液体-多孔饱和介质的弹性动力分析,归结为一个横观各向同性液体-多孔饱和介质在机械荷载作用下的变形问题.自然界中有些物理问题,仅在一个方向发生变形,例如,与变形结构和变形柱有关的问题.土力学中,通常假设只有竖向沉降,从而归结为一维多孔弹性模型.采用各向异性液体-多孔饱和介质的一维变形模型,研究了在不同时间和距离下扰动的变化.给出了在不同类型荷载作用下,介质的各向异性对位移分布和应力分布的影响.     

周围应力与孔隙流体对突出煤力学性质的影响

本文在系统的实验与理论研究基础上,考查了周围应力与孔隙流体对突出煤变形与破坏的影响.提出了一个描述破坏后现象的模型,其判据是一个联系着有效围压与材料强度的无量纲参数.实验表明,吸附瓦斯对应力-应变曲线没有明显影响;有效应力中的孔隙压力项就是游离瓦斯的压力;含气体与液体的多孔介质会有不同有效应力关系.     

非线性塑性材料内部空洞闭合模型的研究

基于典型体元(RVE)模型和Rayleigh-Ritz法,对材料内部空洞从球形闭合成裂纹的过程进行了定量研究.基体材料的本构关系采用幂次粘性方程.通过研究材料变形过程中内部球形空洞和圆形裂纹的演化规律,得到了各自的体积应变率的表达式.采用插值近似,建立了空洞闭合的解析模型,发现空洞变形的主要机理来自于空洞周围基体材料的塑性流动.空洞闭合模型反映了材料属性、远场应力三轴度、远场等效应变对空洞闭合的定量规律.空洞闭合模型的预测结果与文献中的数值结果和有限元计算结果相吻合.空洞闭合模型与CAE(computer-aided engineering)技术相结合可对材料加工工艺进行优化设计,为消除材料内部空洞提供了一条有应用前景的新途径.     

裂缝-孔隙介质中地下水污染问题的Galerkin交替方向有限元方法

考虑裂缝 孔隙介质中地下水污染问题均匀化模型的数值模拟．对压力方程采用混合元方法,对浓度方程采用Ｇａｌｅｒｋｉｎ交替方向有限元方法,对吸附浓度方程采用标准Ｇａｌｅｒｋｉｎ方法,证明了交替方向有限元格式具有最优犔２ 和犎１ 模误差估计．     

细菌堆浸中流动反应传热耦合过程数值模拟分析

针对辉铜矿微生物浸出过程进行数学建模,利用ComsolMultiphysics软件对浸堆中热量传递、氧气流动、目的金属离子分布以及氧化转化率等进行数值模拟分析．结果表明:沿堆体斜坡边界处氧的浓度较大,而在堆的中央部分,氧气的浓度非常小,导致这部分区域浸出反应缓慢;沿浸堆边坡处的温度偏低,温度最高的部分在底部区域附近靠近边坡位置处,且温度升高值超过6℃;矿堆底部靠近边坡区域目的金属离子浓度最高;靠近底部和斜坡部分,浸出反应速率快、氧化转化率高．矿堆的其余部分,因氧浓度低,导致浸出反应速率缓慢、氧化转化率低．     

贫铀合金材料自锻弹丸的数值模拟

利用SPH(Smooth Particle Hydrodynamic)算法对贫铀合金材料自锻弹丸过程进行了数值模拟。其中使用了人造爆轰压力,即给定了爆轰压力的时间分布与空间分布。为了描述材料在高压作用下的变形性能,材料模型采用了Johnson-Cook关系。通过数值计算,给出了自锻弹丸的飞行速度、弹丸几何尺寸及炸高等参数。     

Transmission dynamics of a two-strain pairwise model with infection age

We present and study a two-strain pairwise epidemic model with non-Markovian recovery process in which the recovery rate depends on infection age. The novel model is a hyperbolic system which can be transformed into a system of integro-differential equations by using the method of characteristics. For the two-strain pairwise model, the reproduction number with arbitrary recovery time distributions is obtained. We carry out rigorous analysis and obtain upper and lower estimates for the final epidemic size. Finally, the effects of three commonly used recovery time distributions on the reproduction number are compared by numerical simulations. We further present how the mean length of the infectious period affects the final epidemic size, the peak time and the duration of an epidemic.     

Stokes Flow in Cylindrical Containers With Rotating Ends北大核心CSCD

该文以端部旋转的圆柱形容器内的Stokes流为研究对象,根据流动的特点,将轴向坐标模拟为时间,则问题归结为Hamilton对偶方程的本征值和本征解问题.利用本征解空间的完备性和本征解之间的共轭辛正交关系,给出了问题解的展开形式,并建立了展开系数的数值求解方法.采用该方法研究了单端旋转、两端以相同或相反角速度旋转时不同外形比(容器的高度与半径之比)时圆柱形容器内流动速度和应力的分布情况,展示了不同边界条件下流场的一些特点.     

Numerical solutions of inverse spatial Lotka-Volterra systems

A numerical marching scheme is introduced for the recovery of the solutions and gradient distributions in a one-dimensional nonlinear system of parabolic partial differential equations with space dependent coefficients. In this inverse problem, only Cauchy noisy data at the active boundary is given and no information about the amount and/or character of the noise in the data is assumed. The error analysis for the algorithm is discussed and several numerical examples are presented.     

Convergence analysis of a vertex‐centered finite volume scheme for a copper heap leaching model

In this paper a two‐dimensional solute transport model is considered to simulate the leaching of copper ore tailing using sulfuric acid as the leaching agent. The mathematical model consists in a system of differential equations: two diffusion–convection‐reaction equations with Neumann boundary conditions, and one ordinary differential equation. The numerical scheme consists in a combination of finite volume and finite element methods. A Godunov scheme is used for the convection term and an P1‐FEM for the diffusion term. The convergence analysis is based on standard compactness results in L². Some numerical examples illustrate the effectiveness of the scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

Coupled systems of nonlinear wave equations and finite-dimensional lie algebras I

We study coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability. By making use of Vessiot's geometric theory of differential equations, it is possible to associate to each system of nonlinear wave equations a module of vector fields on the second-order jet bundle — the Vessiot distribution. By imposing certain conditions of the structure of the Vessiot distributions, we identify the so-called separable Vessiot distributions. By expressing the separable Vessiot distributions in a basis of singular vector fields, we show that there are, at most, 27 equivalence classes of such distributions. Of these, 14 classes are associated with Darboux integrable nonlinear systems. We take one of these Darboux integrable classes and show that it is in correspondence with the class of six-dimensional simply transitive Lie algebras. Finally, this later result is used to reduce the problem of constructing exact general solutions of the nonlinear wave equations understudy to the integration of Lie systems. These systems were first discovered by Sophus Lie as the most general class of ordinary differential equations which admit nonlinear superposition principles.     

Recursive equations in finite Markov chain imbedding

In this paper, recursive equations for waiting time distributions of r-th occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and non-overlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov dependent multi-state trials. Using the relationship between number of patterns and r-th waiting time, distributions of number of patterns can also be obtained. The probability generating functions are also obtained. Examples and numerical results are given to illustrate our theoretical results.     

Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.     

The unique solvability of certain multiplicative-convolution equations

In the class of distributions of slow (moderate) growth we consider a class of equations with operations of convolution and multiplication on the real axis. This class contains convolution equations, in particular, ordinary differential equations with constant coefficients, equations in finite differences, functional differential equations with constant coefficients and shifts, and pair differential equations. By virtue of the analytic representation theory for distributions of moderate growth (the Hilbert or Cauchy transform) the class of equations under consideration is equivalent to the class of boundary value problems of the Riemann type, where an equation corresponds to a boundary value condition in the sense of distributions of moderate growth. As a research technique we use the Fourier transform, the generalized Fourier transform (the Carleman-Fourier transform), and the theory of convolution equations in the space of distributions of moderate growth.     

Modelling of stochastic heat transfer in a solid

The unsteady partial differential equations for expectation and correlation distributions of the stochastic temperature distribution in a solid are obtained, when the coefficients and the source term in the stochastic heat transfer equations are white Gaussian processes. Some solutions of the unsteady partial differential equations for expectation and correlation distributions of stochastic heat transfer are presented.