Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier–Stokes equations

In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, Ran and Yuan [On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems, Appl. Math. Comput. 217 (2010), pp. 3050–3068] presented the block symmetric successive over-relaxation (BSSOR) and the modified BSSOR iteration methods based on the special structures of the coefficient matrices. In this study, we present the modified alternating direction-implicit (MADI) iteration method for solving the linear systems. Under suitable conditions, we establish convergence theorems for the MADI iteration method. In addition, the optimal parameter involved in the MADI iteration method is estimated in detail. Numerical experiments show that the MADI iteration method is a feasible and effective iterative solver.     

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.     

Optimum parameter for the SOR-like method for augmented systems

Recently, several proposals for the generalization of Young's SOR method to the saddle point problem or the augmented system has been presented. One of the most practical versions is the SOR-like method given by Golub et al., [(2001). SOR-like methods for augmented systems. BIT, 41, 71–85.], where the convergence and the determination of its optimum parameters were given. In this article, a full characterization of the spectral radius of the SOR-like iteration matrix is given, and an explicit expression for the optimum parameter is given in each case. The new results also lead to different results to that of Golub et al. Besides, it is shown that by the choices of the preconditioning matrix, the optimum SOR-like iteration matrix has no complex eigenvalues, therefore, it can be accelerated by semi-iterative methods.     

四次C-Bézier曲线的拼接技术研究

为了解决造型设计中复杂曲线难以用单一曲线来表示的问题,研究了一种带形状参数的四次C-Bézier曲线的光滑拼接技术.在对四次C-Bézier曲线基函数及其端点性质分析的基础上,给出了两相邻四次C-Bézier曲线间G1、G2和C1、C2的光滑拼接的充要条件,同时还给出了两相邻四次C-Bézier曲线间光滑拼接的基本步骤和几何造型实例.实例结果表明,所提方法简单有效、易实现,极大地增强了四次C-Bézier曲线表达复杂曲线的能力,可广泛地应用于各种CG/CAD/CAID/CAM造型系统中.     

机器学习在河流流量参数估计中的应用

针对经典水位流量关系模型在刻画河流动态变化特性时存在的局限性,提出采用局部加权回归算法估计河流流量;为了提高参数估计精度,提出一种聚类局部加权回归方法。首先对训练样本进行聚类,然后使用k-最近邻方法将新的水位样本划分进最恰当的聚类中,最后估计河流日流量。该方法在估计过程中,避免了不相关信息的干扰,从而提高了日流量数据估计的效率和精度。利用某水文站的实测数据对方法进行测试,仿真结果表明该方法估计精度较高,为水位流量关系模型参数估计提供了新的有效方法。     

脂肪胺聚氧乙烯醚与LAS复配体系的表面活性

研究了脂肪胺聚氧乙烯醚（AE18）和十二烷基苯磺酸钠（LAS）在水溶液中相互作用。通过表面张力法测定了AE18和LAS不同比例下的临界胶束浓度（CMC）。两种表面活性剂以任何比例复配时,复配体系的CMC都明皿低于LAS的CMC;并且在摩尔比n（LAS）：n（AE18）=1：9时,混合体系的CMC比任何单一表面活性剂CMC都低。复配体系达到CMC时的表面张力（γCNC）介于两种表面活性剂之间。运用Clint提出的理想混合胶团公式对CMC值进行了计算,与CMC实验值比较．发现随AE18摩尔分数的增加,CMC的实验值与计算值相近。     

P（3HB-co-4HB）／PLA共混物的扩链改性研究

以异佛尔酮二异氰酸酯（IPDI）和亚磷酸三苯酯（TPP）为扩链剂,对聚（3-羟基丁酸酯-co-4-羟基丁酸酯）／聚乳酸[P（3HB-co-4HB）／（PLA）]共混物进行扩链改性．采用毛细管流变仪、电子万能试验机、差示扫描量热仪和扫描电子显微镜等研究两种扩链剂及用量对扩链前后共混物的流变性能、力学性能、结晶性能及断面形态的影响．结果表明：两种扩链剂均显著提高了共混物的熔体剪切黏度和两组分间的相容性,IPDI和TPP添加量分别为1．5份和1．0份时,改性效果最明显,共混物断裂伸长率及缺口冲击强度分别提高了34．5％、69．6％和89．6％、81．0％;IPDI扩链体系的拉伸强度提高8．3％,而TPP扩链体系的拉伸强度略有下降,表明IPDI扩链效果优于TPP．     

一种与材料状态相关的砂土剪胀性理论模型

结合密砂和中密砂的相变点的概念,提出了以相变状态为参考状态的状态参量表达式,并将此状态参数引入剪胀比的计算公式.在修正剑桥模型的基础上,提出了新的塑性势函数和硬化参数表达式以消除应力路径的影响.在增量塑性理论的基础上,建立了一种适合于密砂和中密砂的与材料状态相关的剪胀性理论模型.     

利用CAE分析注塑工艺参数对薄壁塑件翘曲形变的影响

利用Moldflow软件,分别模拟分析了模温、熔体温度、保压压力和保压时间对聚丙烯（PP）薄壁塑件翘曲形变的影响。结果表明,总体上来说注塑件在中心处的翘曲量最小,而越靠近注塑件边缘则翘曲变形越大。模具温度从40℃提高到60℃,注塑件中心处的翘曲量变小,而注塑件边缘的翘曲量变化不大。熔体温度从230℃提高到250℃,注塑件的翘曲量减小,且对注塑件边缘的翘曲量影响较大。随保压压力提高,注塑件在总体上的翘曲量减小,而浇口区的翘曲量增加。保压时间过短时注塑件在总体上的翘曲量明显较大;保压时间过长则会引起浇口区的翘曲量变大。     

负热膨胀固溶体ZrW_(1.8)V_(0.2)O_(7.9)有序度参数影响因素研究

用酸蒸汽水热-相转变法合成了异价取代W位置的立方ZrW1.8V0.2O7.9固溶体.测定了立方ZrW1.8V0.2O7.9和ZrW2O8在不同温度的晶胞参数和有序度,讨论了ZrW1.8V0.2O7.9和ZrW2O8有序度与保温时间和外界压力之间的关系.结果表明,立方ZrW1.8V0.2O7.9表现出负热膨胀的性质.ZrW1.8V0.2O7.9和ZrW2O8的有序度随保温时间的增长而逐渐变大,真空条件下的有序度高于常压下的有序度.