Implementation of some higher-order convection schemes on non-uniform grids

A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second-order upwind (SOU) scheme and the second-order hybrid scheme (SHYBRID) on non-uniform grids. The implementation method is simple. The accuracy and efficiency of these higher-order schemes on non-uniform grids are assessed. Three well-known bench mark convection-diffusion problems and a fluid flow problem are revisited using non-uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two-dimensional non-linear Burgers equations; and (4) a two-dimensional incompressible Navier-Stokes flow which is similar to the classical lid-driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non-uniform grids. Higher accuracy is obtained for fewer grid points on non-uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non-uniform grid points is properly chosen.     

On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition

In this paper we formulate a theorem on the persistence of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition, and give the measure estimates of parameters for the non-resonance conditions under Rüssmann’s non-degeneracy condition, which is essential for the proof of our result.     

Solvothermal synthesis of TiO2: anatase nanocrystals and rutile nanofibres from TiCl4 in acetone

This work reports a new synthetic approach for single‐phase TiO₂ nanomaterials by solvothermal treatment of titanium tetrachloride in acetone at 80–110 °C. Small, uniform, and yet size‐tunable (5–10 nm) anatase titania nanocrystallites were obtained using a low concentration of TiCl₄ in acetone (i.e., at molar ratios of TiCl₄/acetone ≤ 1:15) in the temperature range of 80–110 °C, while rutile nanofibers were synthesized using a high concentration of TiCl₄ (e.g., TiCl₄/acetone = 1:10) at 110 °C. Copyright © 2007 John Wiley & Sons, Ltd.     

Anchoring Properties of Nematic Liquid Crystals Studied Using the Attenuated Total Reflection Method

By using the attenuated total reflection method associated with the excitation of surface plasmons, the tilt angle of the liquid crystal director and its gradient at the surface are measured in a planar nematic cell as a function of the applied voltage. The surface anchoring anisotropy δπ of the liquid crystal and the surface elastic constant k_s, are found to be δπ = 0.288 erg/cm and k_s, = 9·12 × 10^-11 erg, respectively, when the boundary condition suggested by Barbero et al is used. The theoretical and experimental values obtained with this boundary condition and that of Mada are discussed. The results show that the boundary condition proposed by Barbero et al is in better agreement with the experiment.     

Bipyridinophane‐containing conjugated polymers modulated with an intramolecular aromatic C?H/π interaction

Bipyridinophane–fluorene conjugated copolymers have been synthesized via Suzuki and Heck coupling reactions from 5,8‐dibromo‐2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane and suitable fluorene precursors. Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P7 ) exhibits large absorption and emission redshifts of 20 and 34 nm, respectively, with respect to its planar reference polymer Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐1,4‐(2,5‐dimethylbenzene)] ( P11 ), which bears the same polymer backbone as P7 . These spectral shifts originate from intramolecular aromatic C? H/π interactions, which are evidenced by ultraviolet–visible and ¹H NMR spectra as well as X‐ray single‐crystal structural analysis. However, the effect of the intramolecular aromatic C? H/π interactions on the spectral shift in poly[9,9‐dihexylfluorene‐2,7‐yleneethynylene‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P10 ) is much weaker. Most interestingly, the quenching behaviors of these two conjugated polymers are largely dependent on the polymer backbone. For example, the fluorescence of P7 is efficiently quenched by Cu²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mn²⁺, and Ag⁺ ions. In contrast, only Cu²⁺, Co²⁺, and Ni²⁺ ions can partially quench the fluorescence of P10 , but much less efficiently than the fluorescence of P7 . The static Stern–Volmer quenching constants of Cu²⁺, Co²⁺, and Ni²⁺ ions toward P7 are of the order of 10⁶ M^?1, being 1300, 2500, and 37,300 times larger than those of P10 , respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4154–4164, 2006     

Bioaccumulation and excretion of arsenic compounds by a marine unicellular alga,polyphysa peniculus

Polyphysa peniculus was grown in artificial seawater in the presence of arsenate, arsenite, monomethylarsonate and dimethylarsinic acid. The separation and identification of some of the arsenic species produced in the cells as well as in the growth medium were achieved by using hydride generation–gas chromatography–atomic absorption spectrometry methodology. Arsenite and dimethylarsinate were detected following incubation with arsenate. When the alga was treated with arsenite, dimethylarsinate was the major metabolite in the cells and in the growth medium; trace amounts of monomethylarsonate were also detected in the cells. With monomethylarsonate as a substrate, the metabolite is dimethylarsinate. Polyphysa peniculus did not metabolize dimethylarsinic acid when it was used as a substrate. Significant amounts of more complex arsenic species, such as arsenosungars, were not observed in the cells or medium on the evidence of flow injection–microwave digestion–hydride generation–atomic absorption spectrometry methodology. Transfer of the exposed cells to fresh medium caused release of most cell–associated arsenicals to the surrounding environment.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

氘－氚聚变等离子体中高能α粒子的诊断

本文对于用电荷交换方法或低杂波涨落的方法测量高能α粒子作了简短的评述，建议用核反应１３Ｃ（α，ｎ）１６Ｏ测量氘－氚聚变等离子体中的高能α粒子，并提出了一种减少杂质污染，增加穿透深度的方法。