Koch曲线上的齐次Riemann边值问题

当L为典型的分形曲线一Koch曲线时,提出了Riemann边值问题,但在一般情况下,在Koch曲线上所做的Cauchy型积分无意义.当对已知函数G(z),g(z)增加一定的解析条件,同时利用一列Cauchy型积分的极限函数,对定义在Koch曲线上的齐次Riemann边值问题进行了讨论,并得到与经典解析函数边值问题相类似的结果.     

Tortuosity for streamlines in porous media

An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assumed that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as: c = 0.32, D T c = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.     

Detection of the potential tumor marker of AFP using surface‐enhanced Raman scattering‐based immunoassay

The development of rapid, highly sensitive detection methods for α‐fetoprotein (AFP) is very important. As hepatocellular carcinoma is closely related to the level of AFP in the blood, it is necessary to maintain an AFP concentration below the safety limit. In this paper, we propose a universal, rapid, sensitive, and highly specific immunoassay system utilizing gold nanoparticles (AuNPs) and surface‐enhanced Raman scattering (SERS). This new system features a sandwich structure combining mercaptobenzoic acid‐labeled immunogold nanoparticles with the antigen and the antibody atop a pre‐designed substrate made of a glass slide modified with AuNPs. This SERS‐based immunoassay can detect AFP concentrations as low as 100 pg/ml, which is a significant improvement on the capabilities of the enzyme‐linked immunosorbent assay method. A good linear relationship between the SERS peak intensity and the logarithm of antigen concentrations (from 1 ng/ml to 100 ng/ml) was observed. This technique provides an effective model for the detection of biomarkers in medical diagnostics, criminal investigation, and other fields. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z–c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z–c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.     

Risks of an epidemic in a two-layered railway-local area traveling network

In view of the huge investments into the construction of high speed rails systems in USA, Japan, and China, we present a two-layer traveling network model to study the risks that the railway network poses in case of an epidemic outbreak. The model consists of two layers with one layer representing the railway network and the other representing the local-area transportation subnetworks. To reveal the underlying mechanism, we also study a simplified model that focuses on how a major railway affects an epidemic. We assume that the individuals, when they travel, take on the shortest path to the destination and become non-travelers upon arrival. When an infection process co-evolves with the traveling dynamics, the railway serves to gather a crowd, transmit the disease, and spread infected agents to local area subnetworks. The railway leads to a faster initial increase in infected agents and a higher steady state infection, and thus poses risks; and frequent traveling leads to a more severe infection. These features revealed in simulations are in agreement with analytic results of a simplified version of the model.     

The Effect of Poly(Ethylene Succinate) on Mechanical Properties of PLLA/PES Blend Prepared by Melt-Blending

Fully biodegradable poly(L-lactide) and poly(ethylene succinate) (PLLA/PES) blends were prepared via melt-blending using PLLA and PES as reactants in a stainless steel chamber. The prepared PLLA/PES blend, as well as neat PLLA and PES, was characterized by Fourier transform infrared spectra (FTIR) and X-ray diffraction (XRD) to confirm the structure and the crystallization of PLLA in the blend. The mechanical properties of PLLA/PES blends were determined by bending and tensile tests and the effects of PES content on the mechanical properties of PLLA/PES blends were investigated. It was found that blending some amount of PES could significantly improve the elongation at break while still keeping considerably high strength and modulus. With increasing PES content, both strength and modulus gradually decreased; however the elongation at break significantly increased. SEM was used to examine the morphology of fracture surfaces of PLLA/PES blends.     

The thermal stability of anodic alumina membranes at high temperatures

Nano‐structured anodic alumina membranes are ideal templates and have wide applications. However, anodic alumina materials begin to curl up at high temperatures. To better understand and overcome this problem, the thermal stability of anodic alumina membranes was investigated. Anodic alumina membranes obtained in oxalic acid electrolyte were heat treated in air at different annealing temperatures up to 1200 °C. Our results show that the sub‐pores produced during the annealing process are responsible for the curling. The repulsive forces between neighboring pores caused by mechanical stress at the metal nucleus/oxide interface promote the formation of the sub‐pores. Annealing under a suitable pressure provided thermal stability to the membranes, because it avoided or minimized curling and cracking phenomena. Scanning electron microscopy images showed that the sub‐pores disappeared when annealed under a suitable pressure.     

Effect of growth temperature on the structure and optical properties of ZnO nanorod arrays grown on ITO substrate

ZnO nanorod arrays have been successfully prepared on ITO substrate by a chemical‐bath deposition method at different growth temperatures. The influence of the growth temperature on the morphology and microstructure of the ZnO nanorods was investigated by scanning electron microscopy (SEM) and X‐ray diffraction (XRD). The results showed that the diameter of the ZnO nanorods decreased and the size of the nanocrystals increased with increasing growth temperature. Optical absorption measurements showed the absorption band edge has shifted to a lower‐energy region due to the quantum size effect. Green emission and UV emission bands were observed and they are found to be temperature dependent, which indicates that the deep‐level emission and band‐edge emission of ZnO nanorods is closely related to the rod diameter, and the related mechanism is discussed.     

KBn(n=1~10)团簇的结构和性质的密度泛函理论研究

应用密度泛函理论(DFT) B3LYP方法在6-311+G(d)水平上计算并分析了KBn(n=1~10)团簇的几何结构及电子性质和极化率.通过研究团簇的平均结合能、能级间隙、二阶能量差分分析了团簇的稳定性规律,研究表明: KBn(n=1~10)团簇基态多数为立体构型,能级间隙和二阶能量差分结果表明KB3与KB9是幻数团簇.对团簇基态的极化率研究表明KBn团簇的电子结构随B原子的增加趋于紧凑,基本形成了一定的堆积方式.静态第一超极化率研究表明KB8与KB4两种平面构型的团簇具有较好的非线性光学性能.     

基于光线光学的非线性自聚焦现象的仿真分析

采用光线光学方法对非线性自聚焦现象进行仿真, 能够从宏观上直观地体现强激光的传输过程, 同时避免采用近轴近似、自相似近似等. 本文采用在光传输路径上垂直于光轴切片的方法, 将光的非线性传输转化为切片上的光对折射率的调制作用和切片间的线性传输. 在切片端面上统计光强后对量化误差进行了抑制, 而线性传输过程采用了亚当斯法求解光线方程从而解决了龙格库塔法等不能用于非线性光传输仿真的问题. 仿真结果显示, 强激光自聚焦在轴上有多个焦点, 且第一个焦点的位置随光功率的增大而更靠近入射位置; 由于追迹的是实际光线, 故可以得到近轴区以外区域自聚焦及成丝(环)的情况, 这对于强激光系统安全是有重要意义的. 利用已有的同样基于光线追迹方法的光学设计、仿真软件, 可以把非线性自聚焦介质和线性介质结合起来, 仿真光在实际强激光系统中的传输. 关键词： 实际光线追迹 非线性自聚焦 光传输仿真