An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.     

An active-set projected trust-region algorithm with limited memory BFGS technique for box-constrained nonsmooth equations

In this article, by means of an active set and limited memory strategy, we propose a trust-region method for box-constrained nonsmooth equations. The global convergence and the superlinear convergence are established under suitable conditions.     

Issue Information

An integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of a “molecular rope curtain”: Preparation and characterization of a sliding graft copolymer with grafted poly(ethylene glycol) side chains by the “grafting onto” strategy

A sliding graft copolymer (SGC) with poly(ethylene glycol) (PEG) side chains was prepared by ester formation between terminal carboxyl groups of oxidized PEG methyl ether with molecular weight of 2000 (mPEG2000‐COOH) and hydroxyl groups of a polyrotaxane consisting of PEG and cyclodextrins (CDs). Formation of the SGC structure was confirmed by ¹H NMR, attenuated total reflectance Fourier‐transformed infrared, and gel permeation chromatography. The SGC was soluble in good solvents of PEG and insoluble in poor solvents of PEG. Estimation of the number of grafted mPEG chains suggested a “rope‐curtain” like structure, in which an mPEG chain is connected to each CD ring. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

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简要介绍了中国承担设计和制造任务的ITER计划采购包的构成情况，分析了ITER采购包采用标准的原则和ITER中国采购包引用标准的特点，总结了ITER中国采购包标准化现状。基于当前ITER中国采购包对标准的需求以及着眼于国内磁约束核聚变长远发展需要，讨论提出了当前ITER中国采购包的标准化策略建议。     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.     

中学生学习自我效能感、学习策略与学业成就的关系

以学习自我效能感和学习策略量表为工具,通过方差分析、相关分析和路径分析等方法,重点考察了学习自我效能感和学习策略这两个因素对学业成就的影响路径以及相互间的关系.发现中学生的学习自我效能感与学习策略间存在着显著的相关关系;学习自我效能感和学习策略对初中生的学业成就有显著回归效应,而学习策略对高中生的学业成就有显著回归效应;学习自我效能感可通过影响学习策略来间接影响学业成就.     

Binding numbers for fractional ID-k-factor-critical graphs

LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical(in short,fractional ID-k-factor-critical),if G I has a fractional k-factor for every independent set I of G.The binding number bind(G)of a graph G is defined as bind(G)=min|NG(X)||X|:=X V(G),NG(X)=V(G).In this paper,it is proved that a graph G is fractional ID-k-factor-critical if n≥6k 9 and bind(G)(3k 1)(n 1)kn 2k+2.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

Organic Positive Materials for Magnesium Batteries: A Review

Magnesium batteries, like lithium-ion batteries, with higher abundance and similar efficiency, have drawn great interest for large-scale applications such as electric vehicles, grid energy storage and many more. On the other hand, the use of organic electrode materials allows high energy-performance, metal-free, environmentally friendly, versatile, lightweight, and economically efficient magnesium storage devices. In particular, the structural diversity and the simple activity of organic molecules make redox properties, and hence battery efficiency, easy to monitor. While organic magnesium batteries still in their infancy, this field becomes more and more promising because significant results were reported. To summarize the achievements in studies on organic cathodes for magnesium systems, their synthesis is discussed, combined with electrode design to provide the basis for controlling the electrochemical properties. Moreover, the techniques to synthesize organic materials with high-yield are mentioned. Finally, potential problems and prospects are explored to further improve organic cathodes.