Book reviews

THE BRAIN AND BEHAVIORAL SCIENCES (ISSN 0140-525x).Published quarterly by Cambridge University Press (£35.00).

COMPUTATIONAL PROBABILITY AND SIMULATION by Sidney J.Yakowitz pub. Addison-Wesley Pub. Co. Inc., 1977, pp. 240, £10.00 paperbound £18.00 hardnbound.

THE WORLD FERTILITY SURVEY JAN-DEC 1977-ANNUAL REPORT.

COMPSTAT LECTURES I. LECTURES IN COMPUTATIONAL STATISTICS, Ed. by Horst Skarabis and Peter Sint 1978. 132 pages. Bound, pub. Physica-Verlag, Wurzburg, Germany (DM30).

COMPSTAT 1978. PROCEEDINGS OF 3RD SYMPOSIUM IN COMPUTATIONAL STATISTICS LEIDEN 1978, Ed. by L. C. A.

Corsten and J. Hermans, 1978, 538 pages, Bound, pub. Physica-Verlag, Germany (DM59).     

三维悬链线轨道设计的数值算法

有学者提出了考虑方位漂移的三维悬链线轨道设计问题,并建立了数学模型和数值求解的基本思路,为方位漂移轨道设计技术的应用提供了理论框架,但对求解数学模型的实际算法描述不甚清晰,有可能影响其在大位移井工程设计实践中的广泛应用。考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组,需要使用数值迭代法才能求出其数值解。给出解析形式的垂深增量公式,利用约束方程组中的垂深方程,将3个独立未知数中的一个表示为其他未知数的函数,从而使设计约束方程组可以降维为二元非线性方程组,降低了数值求解的规模和难度。结合隐含未知数的递推计算策略,采用缩半网格法能可靠地求出降维后的设计约束方程组的数值解,特别适用于计算机编程实现。     

Application of the control volume mixed finite element method to a triangular discretization

A two‐dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA.     

Stability of θ-schemes for partial differential equations with piecewise constant arguments of alternately retarded and advanced type

ABSTRACT

This paper deals with the analytical and numerical stability of a partial differential equation with piecewise constant arguments of alternately retarded and advanced type. Firstly, the theory of separation of variables in matrix form and the Fourier method are implemented to achieve the sufficient conditions under which the analytic solution is asymptotically stable. Secondly, the discrete equation is obtained by applying the θ-schemes to the original continuous equation, the sufficient conditions for the asymptotic stability of numerical solution are also shown when the mesh ratio satisfying certain conditions. Finally, some numerical experiments for verifying the theoretical results are provided.     

割缝预抽后煤瓦斯吸附特性的变化特征

为了研究割缝预抽后煤瓦斯吸附特性的变化特征,以杨柳煤矿10煤层7个煤样为研究对象,采用甲烷等温吸附实验测定煤样的Langmuir方程吸附常数a和b,通过压汞实验和低温液氮吸附实验的有机结合,表征煤样孔径分布和比表面积的变化.结果表明:(1)随着煤样与割缝孔距离的增大,吸附常数α呈逐渐增大的趋势,而吸附常数b的变化趋势则相反,但与甲烷等温吸附曲线的曲率变化趋势一致.(2)随着煤样与割缝孔距离的增大,煤样孔径分布发生显著的变化,吸附孔孔容比从33.27％增大到55.38％,比表面积从7.254 m2/g增大到9.856 m2/g.(3)割缝预抽后,煤样参数曲线(Langmuir方程吸附常数、吸附孔孔容比和比表面积)的变化幅度均呈现出平缓→急剧→平缓的趋势,具有有界性和非线性的特征,符合Boltzmann方程.割缝预抽后煤瓦斯吸附特性的变化存在明显的分区特征:变化显著区(小于1.8 m)、变化过渡区(1.8～4.5 m)和变化不显著区(大于4.5 m).(4)割缝预抽后煤体瓦斯压力下降,有效应力增大,进而控制煤体的吸附特性.研究结果可以为煤层水力割缝增透实践提供可靠的基础理论支撑.     

Development of the Hierarchical Domain Decomposition Boundary Element Method for Solving the Three-Dimensional Multiregion Neutron Diffusion Equations

A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the “lower level” calculations. At the “higher level” calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time.     

On the absence of global solutions for quantum versions of Schrödinger equations and systems

We, first, consider the quantum version of the nonlinear Schrödinger equation

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |u(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

where $0<q<1$, $i^q$ is the principal value of $i^q$, $D_{q|t}$ is the $q$-derivative with respect to $t$, $\Delta$ is the Laplacian operator in ${\mathbb{R}}^N$, $\lambda \in ??\left\{0\right\}$, $p>1$, and $u(t,x)$ is a complex-valued function. Sufficient conditions for the nonexistence of global weak solution to the considered equation are obtained under suitable initial data. Next, we study the system of nonlinear coupled equations

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |v(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

$i^q{D}_{q|t}v(t,x)+\Delta v(qt,x)=\lambda |u(qt,x){|}^m,t>0,x\in {\mathbb{R}}^N,$     

多氢酸酸化反应特征及动力学

利用自制多氢酸液XS-1进行静态岩粉溶蚀与岩心流动实验,通过SEM、ICP等实验考察了多氢酸的缓速性与预防二次沉淀性能,并研究了多氢酸与岩心反应动力学特性。结果表明,XS-1多氢酸液具有良好的缓速与预防二次沉淀性能,反应后残酸的极限浓度为0.296 1 mol/L,酸液有效作用时间为6~7 h。在该多氢酸体系下岩心渗透率提高至4.15倍,在此条件下以酸岩反应动力学参数模型建立动力学方程,反应速率比同条件下普通酸液小,进一步证明多氢酸具有一定的缓速性。     

A simulation‐based algorithm for optimal pricing policy under demand uncertainty

We propose a simulation‐based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high‐dimensional parameters, it uses the efficient smoothed functional gradient estimator.     

Wicking into porous polymer-derived ceramic monoliths fabricated by freeze-casting

Silicon oxycarbide monoliths of different pore size distribution were fabricated by freeze-casting. The samples revealed a lamellar pore structure with an axial anisotropy. To evaluate the capillary transport abilities we performed wicking experiments. The sample weight measurement method was applied during the imbibition. The samples show deviations in permeability from 10% to 49% at different sample orientations that quantifies the impact of the anisotropy in the axial direction. The deviations were larger for the samples with smaller pore size. For these samples we also observed larger differences in the wicking behaviour. The samples with bigger pore size demonstrated higher permeability and faster wicking. Imbibition results at both sample orientations showed a good agreement with a prediction via the Lucas–Washburn equation with gravity effects. We demonstrate hereby, that our approach of macroscopic modelling predicts wicking behaviour in anisotropic structures reasonably well, providing a simple tool for further porous material investigations.