Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.     

Guest-Host Type Liquid Crystal Displays

Eight modes of the guest-host cells (GH-cells), in which types of dye, liquid crystal and their alignments are adequately combined, are surveyed, and the color contrast of each mode is calculated.

Three modes among them are of positive type display, that is, colored patterns on the colorless background contrary to the initially proposed fundamental GH-cell. Another three modes are the GH-cells without polarizer, by which bright display can be obtained.

Light stability of dyes are also discussed and lifetimes of various dyes are estimated by accelerated life test. As a result, it is found that diazo-and axomethine-dayes without thiazole groups as well as anthraqunone-dyes have satisfying lifetimes as long as they are used indoors.     

Native agarose gel electrophoresis and electroelution: A fast and cost‐effective method to separate the small and large hepatitis B capsids

Hepatitis B core antigen (HBcAg) expressed in Escherichia coli is able to self‐assemble into large and small capsids comprising 240 (triangulation number T = 4) and 180 (triangulation number T = 3) subunits, respectively. Conventionally, sucrose density gradient ultracentrifugation and SEC have been used to separate these capsids. However, good separation of the large and small particles with these methods is never achieved. In the present study, we employed a simple, fast, and cost‐effective method to separate the T = 3 and T = 4 HBcAg capsids by using native agarose gel electrophoresis followed by an electroelution method (NAGE‐EE). This is a direct, fast, and economic method for isolating the large and small HBcAg particles homogenously based on the hydrodynamic radius of the spherical particles. Dynamic light scattering analysis demonstrated that the T = 3 and T = 4 HBcAg capsids prepared using the NAGE‐EE method are monodisperse with polydispersity values of ～15% and ～13%, respectively. ELISA proved that the antigenicity of the capsids was not affected in the purification process. Overall, NAGE‐EE produced T = 3 and T = 4 capsids with a purity above 90%, and the recovery was 34% and 50%, respectively (total recovery of HBcAg is ～84%), and the operation time is 15 and 4 times lesser than that of the sucrose density gradient ultracentrifugation and SEC, respectively.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Site-selective C–H nitration of N-aryl-7-azaindoles under palladium(II) catalysis

The site-selective C–H nitration reaction of 7-azaindoles with t-butyl nitrite under palladium catalysis is described. This protocol provides an efficient method for the construction of ortho-nitrated N-aryl-7-azaindoles with excellent site-selectivity and functional group compatibility. The formed 7-azaindole derivatives can be readily transformed into 7-azaindoles containing an aniline functional group under palladium-catalyzed hydrogenation conditions.     

Shear-induced band texture of side group liquid crystalline polymers

The shear-induced band texture of conventional end-on fixed side group liquid crystalline polymers (LCPs) has been investigated by using polarizing optical microscopy (POM), small angle light scattering (SALS) and infra-red dichroism techniques. The band spacing is about 1 μm, which increases very slightly on increasing the temperature of shearing and is independent of shearing rate within the range studied. The band texture is not seen to exhibit an interchange of dark and bright bands on rotation of the sample with respect to the polarizer/analyser, but a typical periodical structure is reflected by the SALS patterns of the band texture. The relaxation behaviour of the bands indicates that the band texture formed here is the result of the orderly aligning of domains exhibiting the focal-conic texture, and this is totally different from the case of main chain LCPs where the band texture is substantially an optical effect of the periodic zigzag or sinusoidal structure of parallel aligned microfibrils. Infra-red dichroism and rotating parallel-plate shearing measurements show that the axes of the backbone of the polymer tend to orient in the shearing direction and the end-on fixed mesogenic side groups tend to align perpendicular to the shearing direction.     

Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.     

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Abstract

Stanford Resources Inc., the leading market research firm specializing in the global electronic display industry, has released its annual study on the flat panel display (FPD) industry - Flat lnformation Displays. Now in its eighth edition, this industry perspective analyses competing FPD technologies in terms of technological development, sales, suppliers and future prospects.     

Preparation of Functionalized Imidazolium Salts under Microwave Irradiation

A direct alkylation of a substituted imidazole to prepare the corresponding functionalized ionic liquid has been developed in excellent yields under microwave irradiation.