Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

Synthesis and characterization of a polyfluorene containing carbazole and oxadiazole dipolar pendent groups and its application to electroluminescent devices

We have synthesized a blue‐light‐emitting polyfluorene (PF) derivative ( PF‐CBZ‐OXD ) that presents bulky hole‐transporting carbazole and electron‐transporting oxadiazole pendent groups functionalized at the C‐9 positions of alternating fluorene units. The results from photoluminescence and electrochemical measurements indicate that both the side chains and the PF main chain retain their own electronic characteristics in the copolymer. An electroluminescent device incorporating this polymer as the emitting layer was turned on at 4.5 V; it exhibited a stable blue emission with a maximum external quantum efficiency of 1.1%. Moreover, we doped PF‐CBZ‐OXD and its analogue PF‐TPA‐OXD with a red‐light‐emitting iridium phosphor for use as components of phosphorescent red‐light emitters to investigate the effect of the host's HOMO energy level on the degree of charge trapping and on the electrophosphorescent efficiency. We found that spectral overlap and individual energy level matching between the host and guest were both crucial features affecting the performance of the electroluminescence devices. Atomic force microscopy measurements indicated that the dipolar nature of PF‐CBZ‐OXD , in contrast to the general nonpolarity of polydialkylfluorenes, provided a stabilizing environment that allowed homogeneous dispersion of the polar iridium triplet dopant. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2925–2937, 2007     

Self‐assembly of amphiphilic tris(2,2′‐bipyridine)ruthenium‐cored star‐shaped polymers

Amphiphilic tris(2,2′‐bipyridine)ruthenium‐cored star‐shaped polymers consisting of one polystyrene block and two poly(N‐isopropylacrylamide) blocks were prepared by the “arm‐first” method in which RAFT polymerization and nonconvalent ligand–metal complexation were employed. The prepared amphiphilic star‐shaped metallopolymers are able to form micelles in water. The size and distribution of the micelles were studied by dynamic light scattering and transmission electron microscopy techniques. Preliminary studies indicate that the polymer concentration and the hydrophilic poly(N‐isopropylacrylamide) block length can affect the morphologies of the formed metal‐interfaced core–shell micelles in water. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4204–4210, 2007     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004     

Behavior of cellulose in NaOH/Urea aqueous solution characterized by light scattering and viscometry

Cellulose was dissolved in 6 wt % NaOH/4 wt % urea aqueous solution, which was proven by a ¹³C NMR spectrum to be a direct solvent of cellulose rather than a derivative aqueous solution system. Dilute solution behavior of cellulose in a NaOH/urea aqueous solution system was examined by laser light scattering and viscometry. The Mark–Houwink equation for cellulose in 6 wt % NaOH/4 wt % urea aqueous solution at 25 °C was [η] = 2.45 × 10^?2 weight‐average molecular weight (M_w)^0.815 (mL g^?1) in the M_w region from 3.2 × 10⁴ to 12.9 × 10⁴. The persistence length (q), molar mass per unit contour length (M_L), and characteristic ratio (C_∞) of cellulose in the dilute solution were 6.0 nm, 350 nm^?1, and 20.9, respectively, which agreed with the Yamakawa–Fujii theory of the wormlike chain. The results indicated that the cellulose molecules exist as semiflexible chains in the aqueous solution and were more extended than in cadoxen. This work provided a novel, simple, and nonpollution solvent system that can be used to investigate the dilute solution properties and molecular weight of cellulose. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 347–353, 2004     

The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.     

Effect of end groups on complexation kinetics between cyclodextrins and guest polymers

α‐Cyclodextrin (α‐CD) has been complexed with various poly(ethylene glycol) (PEG) derivatives in aqueous solution. It has been found that the end groups of PEG derivatives affect the complexation kinetics greatly, but have only a little influence on the thermodynamic behavior. By increasing the hydrophobicity of end groups, the complexation speeds up rapidly. On the other hand, the bulky end groups slow down the threading of polymeric guests into the cavity of CD. By changing the hydrophobicity and the size of end groups, the complexation rate can be adjusted in the range of several orders of magnitudes, which should be quite useful in the design of new supramolecular systems. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2050–2057, 2006     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.