On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.     

Effects of simultaneously doped and deposited Ag on the photocatalytic activity and surface states of TiO2

Ag-TiO2 catalysts with different Ag contents were prepared via a sol-gel method in the absence of light. Based on the characterizations of XRD, photoluminescence (PL), surface photovoltage spectroscopy (SPS), field-induced surface photovoltage spectroscopy (FISPS), and XPS as well as the evaluation of the photocatalytic activity for degrading rhodamine B(RhB) solutions, it was found that the Ag dopant promoted the phase transformation as well as had an inhibition effect on the growth of anatase crystallite. The PL and SPS intensities were decreased with increasing Ag content, indicating that the Ag dopant could effectively inhibit the recombination of the photoinduced electrons and holes. However, the active sites capturing the photoinduced electrons reduced, while the Ag content exceeded 5 mol %. At rather low Ag dopant concentrations, the migration and diffusion of Ag+ ions were predominant, while at rather high Ag dopant concentrations, the migration, diffusion, and reduction of Ag ions simultaneously occurred. The Ag-TiO2 photocatalysts with appropriate content of Ag (Ag species concentration is from about 3 to 5 mol %) possessed abundant electron traps so as to be favorable for the separation of the photoinduced electron-hole pairs, which could greatly enhance the activity of the photocatalysts. From the results of FISPS measurements, it could be found that the impurity bands and abundant surface states were introduced into the interfacial layer of TiO2 because of Ag simultaneously doping and depositing, which could improve the absorption capability for visible light of the photocatalysts.     

A donor–acceptor complex enables the synthesis of E-olefins from alcohols,amines and carboxylic acids

Olefins are prevalent substrates and functionalities. The synthesis of olefins from readily available starting materials such as alcohols, amines and carboxylic acids is of great significance to address the sustainability concerns in organic synthesis. Metallaphotoredox-catalyzed defunctionalizations were reported to achieve such transformations under mild conditions. However, all these valuable strategies require a transition metal catalyst, a ligand or an expensive photocatalyst, with the challenges of controlling the region- and stereoselectivities remaining. Herein, we present a fundamentally distinct strategy enabled by electron donor–acceptor (EDA) complexes, for the selective synthesis of olefins from these simple and easily available starting materials. The conversions took place via photoactivation of the EDA complexes of the activated substrates with alkali salts, followed by hydrogen atom elimination from in situ generated alkyl radicals. This method is operationally simple and straightforward and free of photocatalysts and transition-metals, and shows high regio- and stereoselectivities.

A visible-light-induced defunctionalization strategy for the synthesis of olefins by using easily available alcohols, amines and carboxylic acids as starting materials is demonstrated.     

Regio- and stereoselective reactions of a rhodanine derivative with optically active 2-methyl- and 2-phenyloxirane

The reaction of a rhodanine derivative (=(Z)-5-benzylidene-3-phenyl-2-thioxo-1,3-thiazolidin-4-one; 1) with (S)-2-methyloxirane (2) in the presence of SiO₂ in dry CH₂Cl₂ for 10 days led to two diastereoisomeric spirocyclic 1,3-oxathiolanes 3 and 4 with the Me group at C(2) (Scheme 2). The analogous reaction of 1 with (R)-2-phenyloxirane (5) afforded also two diastereoisomeric spirocyclic 1,3-oxathiolanes 6 and 7 bearing the Ph group at C(3) (Scheme 3). The structures of 3, 4, 6, and 7 were confirmed by X-ray crystallography (Figs. 1 and 2). These results show that oxiranes react selectively with the thiocarbonyl group (CS) in 1. Furthermore, the nucleophilic attack of the thiocarbonyl S-atom at the SiO₂-activated oxirane ring proceeds with high regio- and stereoselectivity via an S_N2-type mechanism.     

光条纹中心的实时快速提取

在光电检测系统中,光条纹中心的准确、快速提取是保证系统精度和实时性的必要条件。采用大规模并行算法和串行流水技术,提出了一种基于Steger算法的串并结合的处理结构。该方法在比原算法节省大量逻辑资源的同时,光条纹中心提取速度得到了大大的提升。给出了基于FPGA的实现方法,提取精度达到了亚像素级。