An eigen-based high-order expansion basis for structured spectral elements

We present an eigen-based high-order expansion basis for the spectral element approach with structured elements. The new basis exhibits a numerical efficiency significantly superior, in terms of the conditioning of coefficient matrices and the number of iterations to convergence for the conjugate gradient solver, to the commonly-used Jacobi polynomial-based expansion basis. This basis results in extremely sparse mass matrices, and it is very amenable to the diagonal preconditioning. Ample numerical experiments demonstrate that with the new basis and a simple diagonal preconditioner the number of conjugate gradient iterations to convergence has essentially no dependence or only a very weak dependence on the element order. The expansion bases are constructed by a tensor product of a set of special one-dimensional (1D) basis functions. The 1D interior modes are constructed such that the interior mass and stiffness matrices are simultaneously diagonal and have identical condition numbers. The 1D vertex modes are constructed to be orthogonal to all the interior modes. The performance of the new basis has been investigated and compared with other expansion bases.     

Annealing effect on the ultrafast dynamics of Ag nanoparticles embedded in soda-lime silicate glasses

Ag nanoparticles embedded in soda-lime silicate glasses were fabricated by the ion-exchange technique. Effects of thermal treatment on the optical nonlinearity and ultrafast dynamics of Ag nanoparticles were investigated by applying time-resolved optical Kerr effect and pump-probe techniques. The results indicate that thermal treatment is an efficient method to improve the nonlinear optical performance of this kind of material.     

Post‐Synthetic Polymerization of UiO‐66‐NH2 Nanoparticles and Polyurethane Oligomer toward Stand‐Alone Membranes for Dye Removal and Separation

Metal–organic frameworks (MOFs) are widely used as porous materials in the fields of adsorption and separation. However, their practical application is largely hindered by limitations to their processability. Herein, new UiO‐66‐Urea‐based flexible membranes with MOF loadings of 50 ( 1 ), 60 ( 2 ), and 70 wt % ( 3 ) were designed and prepared by post‐synthetic polymerization of UiO‐66‐NH₂ nanoparticles and a polyurethane oligomer under mild conditions. The adsorption behavior of membrane 3 towards four hydrophilic dyes, namely, eosin Y (EY), rhodamine B (RB), malachite green (MG), and methylene blue (MB), in aqueous solution was studied in detail. It exhibits strong adsorption of EY and RB but weak adsorption of MG and MB in aqueous solution. Owing to the selective adsorption of these hydrophilic dyes, membrane 3 can remove EY and RB from aqueous solution and completely separate EY/MB, RB/MG, and RB/MB mixtures in aqueous solution. In addition, the membrane is uniformly textured, easily handled, and can be reused for dye adsorption and separation.     

Bis‐tert‐Alcohol‐Functionalized Crown‐6‐Calix[4]arene: An Organic Promoter for Nucleophilic Fluorination

A bis‐tert‐alcohol‐functionalized crown‐6‐calix[4]arene (BACCA) was designed and prepared as a multifunctional organic promoter for nucleophilic fluorinations with CsF. By formation of a CsF/BACCA complex, BACCA could release a significantly active and selective fluoride source for S_N2 fluorination reactions. The origin of the promoting effects of BACCA was studied by quantum chemical methods. The role of BACCA was revealed to be separation of the metal fluoride to a large distance (>8 Å), thereby producing an essentially “free” F^?. The synergistic actions of the crown‐6‐calix[4]arene subunit (whose O atoms coordinate the counter‐cation Cs⁺) and the terminal tert‐alcohol OH groups (forming controlled hydrogen bonds with F^?) of BACCA led to tremendous efficiency in S_N2 fluorination of base‐sensitive substrates.     

ZnO–SnO2 branch–stem nanowires based on a two-step process: Synthesis and sensing capability

ZnO–SnO₂ branch–stem nanostructures were realized on a basis of a two-step process. In step 1, SnO₂-stem nanowires were synthesized. In step 2, ZnO-branch nanowires were successfully grown on the SnO₂-stem nanowires through a simple evaporation technique. We have pre-deposited thin Au layers on the surface of SnO₂ nanowire stems and subsequently evaporated Zn powders on the nanowires. The ZnO branches, which sprouted from the SnO₂ stems, had diameters in a range of 30–35 nm. As-synthesized branches were of single crystalline hexagonal ZnO structures. Since the branch tips were comprised of Au-containing nanoparticles, the Au-catalyzed vapor–liquid–solid growth mechanism was more likely to control the growth process of the ZnO branches. To test a potential use of ZnO–SnO₂ branch–stem nanostructures in chemical gas sensors, their sensing performances with respect to NO₂ gas were investigated, showing the promising potential in chemical gas sensors.     

1H and 13C NMR spectral assignments of novel chromenylchalcones

Several types of chalcones containing 2H‐chromen group were synthesized. Claisen–Schmidt condensation of 2H‐chromen‐3‐carbaldehydes (I) with methoxy substituted acetophenones afforded (E)‐3‐(2H‐chromen‐3‐yl)‐1‐(methoxyphenyl)prop‐2‐en‐1‐ones (chromenylchalcones, 1–7). Other types of chromenylchalcone, (E)‐1‐(6‐methoxy‐2H‐chromen‐3‐yl)‐3‐(methoxyphenyl)prop‐2‐en‐1‐ones (8–13) were also obtained between reaction of methoxy substituted benzaldehydes and 1‐(6‐methoxy‐2H‐chromen‐3‐yl)ethanone (II). Dichromenylchalcones (14–16) were also synthesized through the same reaction between aldehydes (I) and ketone (II). Their complete ¹H‐NMR and ¹³C‐NMR assignments are reported here and more polysubstituted chromenylchalcones synthesized or isolated from the natural sources in the future can be identified on the basis of the NMR data reported here. Copyright © 2012 John Wiley & Sons, Ltd.