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.     

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.     

Periodic Solutions of Delay Differential Equations with a Small Parameter: Existence,Stability and Asymptotic Expansion

We consider a scalar delay differential equation with a small parameter, and employ Walthers method to obtain a result on the existence and stability of a slowly oscillatory periodic solution that represents a refinement of the estimate for the Lipschitz constant of a returning map. We also develop a matching method and obtain asymptotic expansions of the slowly oscillatory periodic solution and its minimal period.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthdayAMS subject classifications: 34K15; 34K20; 34C25.     

弹塑性随机振动系统中恢复力数学模型的若干形式

本文基于弹塑性随机振动系统恢复力数学模型的统一形式，提出了能考虑刚度下降段和系统在滞变过程中强度退化的四种恢复力数学模型，为适应系统在多次强随机干扰下的反应分析需要，根据试验结果，提出了经受过强随机干扰的有损伤系统的恢复力模型，并建立了相应的数学表达式，最后针对钢筋砼框架结构在主余震作用下的弹塑性地震反应分析给出了具体算例。