Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

等厚双层涂层材料受集中力作用的平面问题理论解

界面应力的正确评价是分析薄膜涂层材料力学特性的难题之一。利用镜像点法和Dirichlet等值性原理，本文推导了等厚双层薄膜涂层材料受表面集中力作用的平面问题理论解。该显式理论解是以固定在各镜像点上的局部坐标系下的Goursat应力函数的形式给出的。对应于高阶镜像点的应力函数，可通过递推的方法，从对应于低阶镜像点的应力函数求得，而且也易于计算机编程。随着镜像点阶数的增大，它与界面的距离也越来越大，因而相对应的应力函数对界面应力的影响越来越小。最后的算例表明，只需考虑前面有限个镜像点，便可获得足够精度的解。该理论解可作为格林函数，以求解复杂问题的理论解，也可用作边界元法的基本解，提高数值计算的精度和效率。     

On the Hyers-Ulam-Rassias stability of functional equations in n-variables

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form f(φ(X))=?(X)f(X)+ψ(X) and the stability in the sense of Ger for the functional equation of the form f(φ(X))=?(X)f(X), where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers-Ulam-Rassias, Gǎvruta, and Ger for some well-known equations such as the gamma, beta, and G-function type's equations.     

Power scaling of printed-circuit-board preionized TEA CO2 laser up to 3.6 kW

A high average power, high-repetition-rate TEA CO₂ laser employing printed-circuit-board preionizer is described. The power scaling of this preionization configuration has been demonstrated. The average output power reaches 3.6 kW at pulse repetition rate of 180 pps. Furthermore, the scaling-up ability of the rotating spark gap as high-voltage switch for high-average-power gas laser has been validated.     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Magnetotransport and magnetic properties of InAs/Mn digital alloys

We have investigated the magnetic and magneto-transport properties of a systematic sequence of five InAs/Mn digital alloys grown by a combination of molecular beam epitaxy and atomic layer epitaxy. The samples consist of 30 periods of Mn fractional monolayers (ML) (0.17–0.5 ML) separated by 14 ML thick InAs spacer layers in a superlattice configuration. Four samples show n-type electrical conduction while the fifth (0.25 ML Mn) is p-type. Squid magnetization measurements performed on these samples show remnant magnetization above room temperature, which is apparently related to a second phase.     

Structural and dynamic properties of polyoxyethylene sorbitan monooleate micelle in water dispersion studied by pulsed field gradient NMR

The diffusion phenomenon of a nonionic surfactant, polyoxyethylene sorbitan monooleate (POE-SMO), micelle in aqueous solution was investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR) with a high gradient strength of 17.4 T/m at the diffusion timet _d varied from 3 to 300 ms. This high gradient strength allowed us to measure the slow self-diffusion coefficient of POE-SMO micelle, and the short diffusion time below 10 ms showed the restricted diffusion of the micelle. At the shortt _d the self-diffusion of the micelle was restricted and the restricted sizes were 1.8, 1.5, and 0.8 μm for the POE-SMO concentration of 100, 200 and 300 mM, respectively, and 0.6 μm for the POE-SMO only. The possible reason of this restriction was assumed to be the formation of a spatial network or a micellar clustering. Furthermore, a proton exchange between water molecule and surfactant OH group on the micelle surface was proposed. With respect to this proposal, the residence time of the proton at the micelle surface and the thickness of the surface were investigated from proton self-diffusion coefficients by PFG NMR.     

Synthesis and characterization of novel polyimides with 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide

2,2‐Bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide (6FADAP), containing fluorine and phthalimide moieties, was synthesized via the Williamson ether condensation reaction from 1‐chloro‐4‐nitrobenzene and phenolphthalein‐3′,5′‐bis(trifluoromethyl)anilide, which was followed by hydrogenation. Monomers such as 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐anilide containing phthalimide groups and 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein containing only phthalein moieties were also synthesized for comparison. The monomers were first characterized by Fourier transform infrared (FTIR), ¹H NMR, ¹⁹F NMR, elemental analysis, and titration and were then used to prepare polyimides with 2,2‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride. The polyimides were designed to have molecular weights of 20,000 g/mol via off‐stoichiometry and were characterized by FTIR, NMR, gel permeation chromatography (GPC), differential scanning calorimetry, and thermogravimetric analysis. Their solubility, water absorption, dielectric constant, and refractive index were also evaluated. The polyimides prepared with 6FADAP, containing fluorine and phthalimide moieties, had excellent solubility in N‐methylpyrrolidinone, N,N‐dimethylacetamide, tetrahydrofuran, CHCl₃, tetrachloroethane, and acetone, and GPC analysis showed a molecular weight of 18,700 g/mol. The polyimides also exhibited a high glass‐transition temperature (290 °C), good thermal stability (～500 °C in air), low water absorption (1.9 wt %), a low dielectric constant (2.81), a low refractive index, and low birefringence (0.0041). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3361–3374, 2003     

Ultrasonic investigation of amorphous carbon in various frequencies at low temperatures from 2.1 to 300 K

Using pulse echo overlap measurement, the elastic behavior of amorphous carbon has been studied at ambient and low temperatures. The smaller ratio B/G of the bulk modulus to shear modulus and smaller Poisson's ratio σ at room temperature indicate that there is an intrinsic stiffening of transverse acoustic phonons in the amorphous carbon. The acoustic velocity and attenuation for longitudinal modes have been measured between 2.1 and 300 K at three frequencies of 7, 21 and 35 MHz, respectively. Their frequency and temperature dependence are observed. The elastic constant C₁₁ increases with decreasing temperature and show enhanced stiffening at low temperatures. In the 130-220 K region, the abnormal change and effect of longitudinal velocity and attenuation with temperature and frequency, and a phase transition associated with structure relaxations are discussed.