Stabilized Bubble Function Method for Shallow Water Long Wave Equation

A relationship between the stabilized bubble function method and the stabilized finite element method is shown in this paper. The Petrov–Galerkin formulation with bubble function, i.e. a stabilized bubble function method, is proposed for the shallow water long wave equation. The Petrov–Galerkin formulation with the bubble function formulation possesses better stability than the Bubnov–Galerkin formulation with the bubble function.     

Shape optimization of a body located in incompressible flow using adjoint method and partial control algorithm

The purpose of this study is to obtain an optimal shape of a body located in an incompressible viscous flow. The optimal shape of the body is defined so as to minimize the fluid forces acting on it by determining the surface coordinates based on the finite element method and the optimal control theory. The performance function, which is used to judge the optimality of a shape, is defined as the square sum of the drag and lift forces. The minimization problem is solved using an adjoint equation method. The gradient in the adjoint equation is affected by the finite element configuration. The use of a finite element mesh whose shape is appropriate for the procedure is important in shape optimization. If the finite element mesh used is not suitable for computations, the exact gradient is not calculated. Therefore, a structured mesh is used for the adjacent area of the body and all finite element meshes are refined using the Delaunay triangulation at each iteration computation. The weighted gradient method is applied as the minimization technique. Using an algorithm in which all nodal coordinates on the surface of the body are employed and starting from a circle as an initial shape, a front‐edged and rear‐round shape is obtained because of the vortices at the back of the body. To overcome this difficulty, we introduced the partial control algorithm, in which some of the nodal coordinates on the surface of the body are updated. From four cases of computational studies, we reveal that the optimal shape has both sharp front and sharp rear edges. All computations are conducted at Reynolds number Re=250. The minimum value of the performance function is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Photoreactive nanomatrix structure formed by graft‐copolymerization of 1,9‐nonandiol dimethacrylate onto natural rubber

Formation of photoreactive nanomatrix structure was investigated by graft‐copolymerization of an inclusion complex of 1,9‐nonandiol dimethacrylate (NDMA) with β‐cyclodextrin (β‐CD) onto natural rubber particle using potassium persulfate (KPS), tert‐butyl hydroperoxide/tetraethylenepentamine (TBHPO/TEPA), cumene hydroperoxide/tetraethylenepentamine (CHPO/TEPA), and benzoyl peroxide (BPO) as an initiator. The graft copolymer was characterized by ¹H NMR and FTIR after coagulation. The conversion of NDMA and the amount of residual methacryloyl group were found to be 58.5 w/w % and 1.81 w/w %, respectively, under the suitable condition of the graft‐copolymerization. The morphology of the film specimen, prepared from the graft copolymer, was observed by transmission electron microscopy (TEM) after staining the film with OsO₄. Natural rubber particle of about 1.0 μm in diameter was dispersed in poly(NDMA) matrix of about 10 nm in thickness. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2418–2424, 2010     

Mechanism for the direct synthesis of tryptophan from indole and serine: a useful NMR technique for the detection of a reactive intermediate in the reaction mixture

The reaction mechanism for the biomimetic synthesis of tryptophan from indole and serine in the presence of Ac₂O in AcOH was investigated. Although the time‐course ¹H‐NMR spectra of the reaction of 5‐methoxyindole with N‐acetylserine were measured in the presence of (CD₃CO)₂O in CD₃CO₂D, the reactive intermediate could not be detected. This reaction was conducted without 5‐methoxyindole in order to elucidate the reactive intermediate, but the intermediate could not be isolated from the reaction mixture. Since the intermediate would be expected to have a very short life time, and therefore be very difficult to detect by conventional analytical methods, the structure of the intermediate was elucidated using a 2D‐NMR technique, diffusion‐ordered spectroscopy (DOSY). Two intermediates were detected and confirmed to be 2‐methyl‐4‐methyleneoxazol‐5(4H)‐one and 2‐methyl‐4‐hydroxymethyloxazol‐5(4H)‐one. The present results demonstrated that DOSY is a powerful tool for the detection of unstable intermediates. Copyright © 2010 John Wiley & Sons, Ltd.     

In situ x-ray diffraction measurements of the capillary fountain jet produced via ultrasonic atomization

In situ x-ray diffraction measurements were carried out for investigating the liquid structure in the ultrasonic fountain jet to consider the mechanism of the "ultrasonic ethanol separation" reported by Sato et al. [J. Chem. Phys. 114, 2382 (2001)]. For pure liquids (water and ethanol), it was found that the high frequency ultrasound does not affect the liquid structure microscopically. For the 20 mol % ethanol-water mixture, the estimated ethanol mole fraction in the ultrasonic fountain jet by using the position of the main maximum in the x-ray diffraction profile coincided with that in the reservoir. This result suggests that the ethanol separation is not caused by any distorted liquid structure under the ultrasound irradiation and occurs when or after the generation of the liquid droplet mist.     

Chemoenzymatic synthesis of sacranosides a and B

Direct beta-glucosidation between (-)-myrtenol and nerol and D-glucose (3) using the immobilized beta-glucosidase from almonds with the synthetic prepolymer ENTP-4000 gave myrtenyl O-beta-D-glucoside (4) and neryl O-beta-D-glucoside (10), respectively. The coupling of the myrtenyl or neryl O-beta-D-glucopyranoside congeners (7 or 13) and 2,3,4-tri-O-benzoyl-beta-L-arabinopyranosyl bromide (8) afforded the coupled products (9 or 14), respectively. Deprotection of the coupled products (9 or 14) afforded the synthetic myrtenyl 6-O-alpha-L-arabinopyranosyl-beta-D-glucopyranoside (Sacranoside A, 1) or neryl 6-O-alpha-L-arabinopyranosyl-beta-D-glucopyranoside (Sacranoside B, 2), respectively.