Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

离散Lyapunov矩阵方程X—AXB=C的一种数值解法

本文提供了求解离散Lyapunov矩阵方程的一种数值解法。首先讨论了系数矩阵为三对角形矩阵的公式解法,然后通过相似变换,将该方法推广到一般情形。     

带相变的铸坯热弹塑性应力分析基本方程

本文讨论了温度、相变、应力间的耦合关系，给出了铸坯在考虑相变时的热弹塑性蠕变的本构关系，以及计算铸坯内应力的有限元迭代公式。     

STABLE DOUBLE LR ALGORITHM AND ITS ERROR ANALYSIS

In this paper, the normative matrices and their double LR transformation with origin shifts are defined, and the essential relationship between the double LR transformation of a normative matrix and the QR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double LR algorithm for double LR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double LR algorithm for normative matrices is only four sevenths of the rational QR algorithm for reed symmetric tridiagonal matrices.     

CHAOS FOR MIXING TRANSFORMATIONS

ＣＨＡＯＳＦＯＲＭＩＸＩＮＧＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳ￥ＬＩＡＯＧＯＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈａｎｇｃｈｕｎ１３００２３,Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｆｏｒａｃｌａｓｓｏｆｍ...     

关于全图补图的完美匹配

G是一个简单图,变换图G---是G的全图的补图.证明了对于给定的一个图G,G K1 K2,G---有一个完美匹配的充要条件是V(G) E(G)是偶数.     

用非最大纠缠态实现三粒子纠缠态的几率隐形传输

提出一种利用三对非最大纠缠态粒子作为量子通道来传输三粒子纠缠态的方案。在此方案中发送者Alice作三次Bell态测量,并将测量结果通过经典通道告诉Bob,B。b根据接收到的信息即可通过相应的幺正变换来重建Alice要传输的量子态。     

振荡型积分对极大函数的估计

首先将2维KaKeya型的极大函数通过Fourier变换转化成振荡型积分的形式,对此振荡型积分作相应的估计。通过Littlewood—Paley方法将此振荡型积分分解成不同的算子,在估计极大算子时,通过Newton—Leibnig公式,将其转化为相应的积分形式,最后通过经典的振荡型积分的估计,得到最后的结果,本方法强调振荡型积分的方法和以前几何测度论的方法不同。     

Phase stability and temperature effect in ScX (X=S,Se and Te) compounds

Based on first-principles calculations, the structural stability and temperature effect in ScX (X=S, Se and Te) compounds are studied with three typical structures of B1 (NaCl-type), hcp (NiAs-type) and β-hcp (inverse Li₂O₂-type). Their dynamic stability has been verified using phonon mode analysis and molecular dynamics simulations. From the total energy calculations, we find that the most stable ground state structures are B1 for ScS, and hcp for ScSe and ScTe, respectively. Moreover, structural stabilities at finite temperature are studied with the combination of phonon dependent dynamics analysis and first-principles calculations, which reveals a phase transition from hcp to B1 in ScSe around 230 K and a phase transition from hcp to β-hcp in ScTe around 460 K, in accordance with experimental findings. The energy barrier and pathway along the phase transformation from hcp to β-hcp ScTe are also calculated and analyzed by the solid-state nudged elastic band method.     

A study on the phase transformation behaviour of Cu-20wt.Sn alloy produced using powder metallurgy method: Experimental and molecular dynamics modelling

In this study, Cu-20wt.Sn alloy was produced by powder metallurgy (PM) method by using high purity element powders. The phases in the microstructure of the produced alloy were determined by XRD study. The phase transformation behaviour of the alloy was investigated by DSC and modelling method. Moreover, the Cu-20wt.Sn alloy system was modelled with molecular dynamics (MD) simulation based on modified Embedded Atom Method (MEAM). The radial distribution function (RDF) was calculated to determine the structural properties of system during the phase transformations. The experimental results showed that the transformation ($\alpha +\delta$) → ($\alpha +\gamma$) occur at temperature above 500°C. The simulation results showed that the phase transformation $\alpha +\delta \to \alpha +\gamma$ occurs at 550°C temperature. Our simulation results are in reasonable agreement with the experimental data.