A Two‐Parameter Stabilized Finite Element Method for Incompressible Flows

Based on two‐grid discretizations, a two‐parameter stabilized finite element method for the steady incompressible Navier–Stokes equations at high Reynolds numbers is presented and studied. In this method, a stabilized Navier–Stokes problem is first solved on a coarse grid, and then a correction is calculated on a fine grid by solving a stabilized linear problem. The stabilization term for the nonlinear Navier–Stokes equations on the coarse grid is based on an elliptic projection, which projects higher‐order finite element interpolants of the velocity into a lower‐order finite element interpolation space. For the linear problem on the fine grid, either the same stabilization approach (with a different stabilization parameter) as that for the coarse grid problem or a completely different stabilization approach could be employed. Error bounds for the discrete solutions are estimated. Algorithmic parameter scalings of the method are also derived. The theoretical results show that, with suitable scalings of the algorithmic parameters, this method can yield an optimal convergence rate. Numerical results are provided to verify the theoretical predictions and demonstrate the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 425–444, 2017     

Mixed homopolymer brushes grafted onto a nanosphere

Microphase separation of mixed A∕B polymer brushes grafted onto a nanosphere with its radius comparable to the size of polymers is investigated by numerical implementation of the self-consistent field theory. The idea is to embed the sphere within a larger cubic computational cell and use a "masking" technique to treat the spherical boundary. The partial differential equations for the chain propagator on the sphere can thus be readily solved with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on a cubic cell. This numerical technique can circumvent the "pole problem" due to the use of a spherical coordinate system in conventional finite difference or finite element grid. We systematically investigate the effect of the total grafting density, composition, chain length asymmetry between two grafted homopolymers as well as spherical radius, i.e., substrate curvature on the formation of island structure with specific arrangement in a regular lattice. A series of island structures with different island numbers representing specific structure symmetry ranging from 2 to 12 except for 11 are found, in contrast to conventional hexagonal arrangement for polymer brushes on a planar substrate. Among these parameters, the spherical radius plays a significant role in determining the type of island structures, i.e., the morphology formed on the sphere.     

A fast technique applied to the analysis of Resistive Wall Modes with 3D conducting structures

This paper illustrates the development of a “fast” technique for the analysis of Resistive Wall Modes (RWMs) in fusion devices with three-dimensional conducting structures, by means of the recently developed CarMa code. Thanks to its peculiar features, the computational cost scales almost linearly with the number of discrete unknowns. Some large scale problems are solved in configurations of interest for the International Thermonuclear Experimental Reactor (ITER).     

Modulation of the work function of fullerenes C60 and C70 by alkali-metal adsorption: A theoretical study

The impact of alkali-metal (Li/Na/Cs) adsorption on work function of fullerenes C₆₀ and C₇₀ was investigated by first-principles calculations. After adsorption, the work functions of fullerenes C₆₀ and C₇₀ decrease distinctly and vary linearly with the electronegativity of the alkali metal elements, and the positions where the alkali atoms are adsorbed considerably influence the work functions. On the contrary, a vacancy defect elevates the work functions of the fullerenes C₆₀ and C₇₀. The variation in the work functions rests with variation in Fermi level (which are attributed to charge transfer) and variation in vacuum levels (which are attributed to the induced dipole moments). Moreover, alkali-metal adsorption can also improve the electric conductivity of a fullerene mixture of C₆₀ and C₇₀.     

Removal of Toluene from Industrial Gas by Adsorption–Plasma Catalytic Process: Comparison of Closed Discharge and Ventilated Discharge

Degradation of adsorbed toluene over 13X zeolite, 5A molecular sieve and Al₂O₃ by non-thermal plasma was investigated. Different discharge modes, including closed and ventilated discharge were compared. The carbon balance and COx yield of 13X zeolite were increased by 17.6 and 19.4% by ventilated discharge, respectively, compared with closed discharge. But for 5A molecular sieve and Al₂O₃, the carbon balance and COx yield by closed discharge were greater than those by ventilated discharge. It meant that the closed discharge was more suitable for low-concentration of VOC and the residence time of reactants would be prolonged. Removal of high-concentration VOC by ventilated discharge was more appropriate because of more reactive oxygen species generated. Furthermore, the effect of discharge background gas was studied. Removal of adsorbed toluene over Co/13X by oxygen and air with different flow rate as background gas were compared. The removal efficiency was reduced as flow rate of background gas increased. The oxygen-discharge was more efficiency for toluene oxidation and inhibited the generation of nitrogen oxides.     

The stereoselective synthesis of e‐1,2‐bis(3‐indolizinyl)ethylenes by the reactions of 3‐thioformylindolizines with n‐tributylphosphine

3‐Thioformylindolizines undergo novel reductive coupling reaction in the presence of tributylphosphine to give E‐1,2‐bis(3‐indolizinyl)ethylenes in high yield. These reactions proceed via (3‐indolizinyl)methylene carbene intermediate and provide a new, stereoselective synthesis of the bis(3‐indolizinyl)ethylene derivatives highly.     

大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性.     

Apparently enhanced magnetization of Cu(I)-modified <Emphasis Type="Italic">γ</Emphasis>-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> based nanoparticles

Using a chemically induced transition method in FeCl₂ solution, γ-Fe₂O₃ based magnetic nanoparticles, in which γ-Fe₂O₃ crystallites were coated with FeCl₃?6H₂O, were prepared. During the synthesis of the γ-Fe₂O₃ nanoparticles Cu(I) modification of the particles was attempted. According to the results from both magnetization measurements and structural characterization, it was judged that a magnetic silent “dead layer”, which can be attributed to spin disorder in the surface of the γ-Fe₂O₃ crystallites due to breaking of the crystal symmetry, existed in the unmodified particles. For the Cu(I)-modified sample, the CuCl thin layer on the γ-Fe₂O₃ crystallites incurred the crystal symmetry to reduce the spin disorder, which “awakened” the “dead layer” on the surface of the γ-Fe₂O₃ crystallites, enhancing the apparent magnetization of the Cu(I)-modified nanoparticles. It was determined that the surface spin disorder of the magnetic crystallite could be related to the coating layer on the crystallite, and can be modified by altering the coating layer to enhance the effective magnetization of the magnetic nanoparticles.     

Fe-C纳米微粒的透射电镜观察与选区电子衍射分析

利用透射电镜观察和选区电子衍射分析研究了在18kPa的Ar气氛中通过交流电弧法制备的Fe -C纳米微粒。结果表明微粒主要为两种类型 :一类是FeC合金微粒 ,另一类是具有氧化层结构的Fe微粒 ,不同粒径的微粒类呈现不同聚集特性。