大型液相色谱分离过程FAD－SMT数学模型及其数值解

提出大型液相色谱分离过程ＦＡＤ－ＳＭＴ数学模型，把色谱分离连续性方程转变为对流扩散方程和常微分方程组，并提出模型的数值方法，分析了数值解的稳定条件和收敛条件以及空间和时间步长的选取。实验结果表明，ＦＡＤ－ＳＭＴ数学模型计算的液相色谱分离葡萄糖、果糖和分离甘露醇、山梨醇理论与实验流出曲线相吻合。灵敏度分析结果表明：相平衡常数比轴向扩散系数和总传质系数对色谱分离有较大的影响。     

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

数控仿形系统中的数字化技术

利用仿形仪扫描模型表面,自动生成描述模型表面的数控指令,实时转存到软磁 盘中。利用上述的数字化结果在数控功能支持下进行数字化加工,可以加工出各轴独 立改变比例的工件和镜像的工件,也可以实现阴阳模工件的配对加工。数字化技术在 模具及复杂表面加工中有童要意义。     

Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

In this paper we consider the Dirichlet problemwhere $\rho$ is a small parameter and $\Omega$ is a $C^2$ bounded domain in $\mathbb{R}^2$. In [1], the author proves the existence of a $m$-point blow-up solution $u_\rho$ jointly with its asymptotic behaviour. We compute the Morse index of $u_\rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.     

Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

砂土中螺旋桩在斜拉荷载作用下的承载性能

为研究斜拉荷载倾斜角度和叶片埋深对螺旋桩极限承载力的影响,基于ABAQUS软件构建了砂土中螺旋桩的有限元模型,通过螺旋桩水平承载机理砂箱试验与竖向拉拔试验数据,对模型的准确性和可行性进行验证。设置4组不同叶片埋深的螺旋桩模型,分别施加不同角度的斜拉荷载,探讨了砂土地基中螺旋桩的承载性能与斜拉角度、叶片埋深的相关性。结果表明:砂土中螺旋桩的极限承载力随着斜拉角度的增大不断减小;当斜拉角度小于30°时,螺旋桩极限承载力与斜拉角度的关系曲线近似呈线性;螺旋桩极限承载力存在一个临界埋深比,当埋深比大于等于4时,承载力不随埋深比的增大而变化。推导了深埋状态下螺旋桩受斜拉荷载作用的极限承载力公式,经验证该公式能较好反映螺旋桩极限承载力随斜拉角度增大而逐渐下降的规律。     

垂直弹射系统弹射初始阶段内流场数值分析

针对燃气活塞弹射装置在垂直发射系统中的应用,采用计算流体软件Fluent的源项法,用UDF(用户自定义函数)编译来实现火药燃气的质量、动量、能量向高压室的注入,对弹射初始阶段高压室和低压室内燃气流场进行了数值分析,得出以下结论:高压室压力在破膜前快速上升,破膜后缓慢上升的趋势,在高压上下两端压力应力集中,低压室呈中间和两端压力应力集中现象,同时高压室形成的低速燃气经导管产生激波形成超声速燃气流撞击低压室,并分析了压力和速度对弹射装置的影响。计算结果表明,该方法能够较好地仿真弹射装置燃气流场的特性,为弹射装置优化设计和装药设计提供理论依据。     

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

Sea water intrusion and salt water intrusion in the coastal area of Laizhou Bay

The characteristics, pattern, hydrodynamic and hydrochemical features, and the movement pattern of the salt waterfresh water interface of the sea water intrusion and the salt water intrusion, which occur in the coastal area of Laizhou Bay in Shandong Province, are analysed. The characteristics of the two kinds of intrusion are compared as well. A three-dimensional sea water intrusion model to describe the sea water intrusion with a transitional zone 1.5–6.0 km wide in the phreatic aquifer and a solute transport model describing the behavior of cations exchange in the process of sea water intrusion are established.