Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

对正负一级能量之比测量光栅参量方法的改进

提出利用同一波长的入射光在双面入射时两个能量之比的比值对光栅的参量进行测量,进一步提高准确度。首先从理论上比较正弦面形光栅在单一面入射及双面入射时各种衍射效率对光栅表面粗糙度的敏感程度;然后模拟测量出该正弦面型光栅在双面入射情况下的光栅参量;最后成功反演出体积相位全息光栅的三个参量,其测量结果为0.080μm,1.452μm,20.5μm准确度比单一入射面情况(0.080μm,1.451μm,20.1μm)时要高。同时该法继承了原来方法的无损伤、操作简便、可重复、易推广、成本低等优点。     

A metastable flame-front interface and Carrier''s problem

Metastable dynamics for a nonlocal PDE modeling the upwards propagation of a flame-front interface in a vertical channel is analyzed in the one-dimensional case where the channel cross-section is taken to be the slab -1<x<1. In a certain asymptotic limit, the interface assumes a roughly concave parabolic shape, and the tip of the parabola drifts asymptotically exponentially slowly towards the boundary of the domain. In contrast to previous analyses that studied this behavior by transforming the governing nonlocal PDE to a convection–diffusion equation, a novel nonlinear transformation is introduced that transforms the problem to a singularly perturbed quasilinear PDE. The steady-state problem for this transformed PDE, for which the parabolic interface shape maps onto a one-spike solution, is closely related to a class of two-point boundary value problems with seemingly spurious solutions studied initially by G. Carrier in 1968. Rigorous and formal asymptotic results for a one-spike solution to this transformed PDE are obtained together with a formal metastability analysis of certain time-dependent solutions.     

High-energy scale revival and giant kink in the dispersion of a cuprate superconductor

In the present photoemission study of a cuprate superconductor Bi1.74Pb0.38Sr1.88CuO6+delta, we discovered a large scale dispersion of the lowest band, which unexpectedly follows the band structure calculation very well. Similar behavior observed in blue bronze and the Mott insulator Ca2CuO2Cl2 suggests that the origin of hopping-dominated dispersion in an overdoped cuprate might be quite complicated. A giant kink in the dispersion is observed, and the complete self-energy containing all interaction information is extracted for a doped cuprate. These results recovered significant missing pieces in our current understanding of the electronic structure of cuprates.     

A New Method for Establishing Pseudo Orthogonal Properties of Eigenfunction Expansion Form in Fracture Mechanics

A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal …     

Green Approach to the Fabrication of Superhydrophobic Mesh Surface for Oil/Water Separation

We report a simple and environment friendly method to fabricate superhydrophobic metallic mesh surfaces for oil/water separation. The obtained mesh surface exhibits superhydrophobicity and superoleophilicity after it was dried in an oven at 200 °C for 10 min. A rough silver layer is formed on the mesh surface after immersion, and the spontaneous adsorption of airborne carbon contaminants on the silver surface lower the surface free energy of the mesh. No low‐surface‐energy reagents and/or volatile organic solvents are used. In addition, we demonstrate that by using the mesh box, oils can be separated and collected from the surface of water repeatedly, and that high separation efficiencies of larger than 92 % are retained for various oils. Moreover, the superhydrophobic mesh also possesses excellent corrosion resistance and thermal stability. Hence, these superhydrophobic meshes might be good candidates for the practical separation of oil from the surface of water.     

A three‐dimensional cadmium(II) coordination polymer with unequal homochiral double‐stranded concentric helical chains

A homochiral helical three‐dimensional coordination polymer, poly[[(μ₂‐acetato‐κ³O,O′:O)(hydroxido‐κO)(μ₄‐5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ido‐κ⁵N¹,O:N²:N⁴:N⁵)(μ₃‐5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ido‐κ⁴N¹,O:N²:N⁴:N⁵)dicadmium(II)] 0.75‐hydrate], {[Cd₂(C₇H₅N₆O)₂(CH₃COO)(OH)]·0.75H₂O}_n, was synthesized by the reaction of cadmium acetate, N‐(1H‐tetrazol‐5‐yl)isonicotinamide (H‐NTIA), ethanol and H₂O under hydrothermal conditions. The asymmetric unit contains two crystallographically independent Cd^II cations, two deprotonated 5‐nicotinamido‐1H‐1,2,3,4‐tetrazol‐1‐ide (NTIA⁻) ligands, one acetate anion, one hydroxide anion and three independent partially occupied water sites. The two Cd^II cations, with six‐coordinated octahedral and seven‐coordinated pentagonal bipyramidal geometries are located on general sites. The tetrazole group of one symmetry‐independent NTIA⁻ ligand links one of the independent Cd^II cations into 6₁ helical chains, while the other NTIA⁻ ligand links the other independent Cd^II cations into similar but unequal 6₁ helical chains. These chains, with a pitch of 24.937 (5) Å, intertwine into a double‐stranded helix. Each of the double‐stranded 6₁ helices is further connected to six adjacent helical chains through an acetate μ₂‐O atom and the tetrazole group of the NTIA⁻ ligand into a three‐dimensional framework. The helical channel is occupied by the isonicotinamide groups of NTIA⁻ ligands and two helices are connected to each other through the pyridine N and carbonyl O atoms of isonicotinamide groups. In addition, N—H...O and O—H...N hydrogen bonds exist in the complex.     

TiO2修饰La0.6Sr0.4Co0.2Fe0.8O3-δ用于中温固体氧化物燃料电池的阴极

纳米TiO2修饰的La0.6Sr0.4Co0.2Fe0.8O3-δ(LSCF)阴极被直接应用于YSZ电解质电池上. TiO2可阻止LSCF和YSZ间的化学反应,抑制SrZrO3的形成. LSCF-0.25 wt% TiO2阴极电池在0.7 V和600°C下的电流密度是LSCF阴极电池的1.6倍.电化学阻抗谱结果表明, TiO2修饰显著加快了氧离子注入电解质的过程,这可能与TiO2抑制了阴极/电解质界面处高电阻SrZrO3层的形成有关.本文为在ZrO2基电解质上使用高性能的(La,Sr)(Co,Fe)O3阴极材料提供了一种简单有效的方法.     

Dual Esterase‐ and Steroid‐Responsive Energy Transfer Modulation of Ruthenium(II) and Rhenium(I) Complex Functionalized Gold Nanoparticles

A number of adamantane‐containing ruthenium(II) and rhenium(I) complexes have been synthesized, characterized, and noncovalently functionalized with β‐cyclodextrin‐capped gold nanoparticles (β‐CD–GNPs) through the host–guest interaction between cyclodextrin and adamantane. The resultant nanoconjugates have been characterized by transmission electron microscopy (TEM), energy‐dispersive X‐ray analysis (EDX), and 2D ROESY ¹H NMR experiments. The Förster resonance energy transfer (FRET) properties of the nanoconjugates can be modulated by both esterase‐accelerated hydrolysis and competitive displacement of steroid, by monitoring the emission intensity and luminescence lifetime. The FRET efficiencies are found to vary with the nature of the chromophores and the length of the spacer between the transition metal complexes and the GNPs. This work constitutes a “proof‐of‐principle” assay method for the dual‐functional detection of important classes of biomolecules, such as enzymes and steroids.     

聚苯氧基磷酸联苯二酚酯/聚磷酸铵膨胀阻燃剂对环氧树脂阻燃性能影响研究

以聚苯氧基磷酸联苯二酚酯(PBPP)与聚磷酸铵(APP)组成复合阻燃剂,对环氧树脂(EP)进行阻燃改性.通过氧指数(LOI)、垂直燃烧(UL-94)、热失重(TGA)、锥形量热(CONE)和扫描电镜(SEM)等方法研究改性环氧树脂的阻燃性能和阻燃机理.结果表明,PBPP/APP体系对EP具有较好的阻燃性能,阻燃剂添加量为10%时能使环氧树脂的氧指数提高到29.6%,垂直燃烧等级达到UL94 V-0级,残炭量大大增加;平均热释放速率下降45.7%,热释放速率峰值下降51.0%,有效燃烧热平均值下降21.1%;TGA、CONE、SEM等综合分析显示了PBPP/APP改性后的环氧树脂比纯环氧树脂具有更高的热稳定性,燃烧后能够形成连续、致密、封闭、坚硬的焦化炭层,在聚合物表面产生有效覆盖、隔绝了氧气,改善了环氧树脂的燃烧性能.