The two‐dimensional streamline upwind scheme for the convection–reaction equation

This paper is concerned with the development of the finite element method in simulating scalar transport, governed by the convection–reaction (CR) equation. A feature of the proposed finite element model is its ability to provide nodally exact solutions in the one‐dimensional case. Details of the derivation of the upwind scheme on quadratic elements are given. Extension of the one‐dimensional nodally exact scheme to the two‐dimensional model equation involves the use of a streamline upwind operator. As the modified equations show in the four types of element, physically relevant discretization error terms are added to the flow direction and help stabilize the discrete system. The proposed method is referred to as the streamline upwind Petrov–Galerkin finite element model. This model has been validated against test problems that are amenable to analytical solutions. In addition to a fundamental study of the scheme, numerical results that demonstrate the validity of the method are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Synthesis and Cytotoxic Activities of α‐Methylidene‐γ‐butyrolactones Bearing a Quinolin‐4(1H)‐one Moiety

The cytotoxicities of the α‐methylidene‐γ‐butyrolactones 4 , 5 , and 8 , which are linked to a quinolin‐4(1H)‐one moiety through a piperazine or O‐atom bridge were studied. These compounds were synthesized by alkylation of 1‐ethyl‐6‐fluoro‐1,4‐dihydro‐7‐hydroxy‐4‐oxoquinoline‐3‐carboxylic acid ( 6 ) followed by a Reformatsky‐type condensation. Compounds 4 , 5 , and 8 were evaluated in vitro against 60 human‐tumor cell lines derived from nine cancer‐cell types and demonstrated not only strong growth‐inhibitory activities against leukemia cancer cells, but also fairly good activities against the growth of certain solid tumors (see Table). The O‐bridged derivatives 8a and 8b exhibit both cytostatic (mean log GI₅₀=−5.20 and −5.82, resp.) and cytocidal (mean log LC₅₀=−4.30 and −4.93, resp.) effects, while the piperazine‐bridged analogues 4 and 5 possess only weak cytostatic (mean log GI₅₀=−5.19 and −4.74, resp.; mean log LC₅₀>−4.00) capability. Among them, 8b is the most potent, with log GI₅₀=−6.47, −6.72, −6.53, and −6.52 against leukemia, SW‐620 (colon), Lox IMV1, and SK‐MEL‐28 (melanoma) cancer cells, respectively.     

Separation of Anthraquinones by Capillary Electrophoresis and High‐Performance Liquid Chromatography

The separation and determination of twelve anthraquinones, viz. anthraquinone 1, chrysphanol 2, aloe‐emodin 3, alizarin 4, anthraquinone‐2‐carboxylic acid 5, purpurin 6, sennoside B 7, sennoside A 8, emodin 9, quinalizarin 10, rhein 11, and anthraflavic acid 12, were achieved by capillary electrophoresis (CE) and high‐performance liquid chromatography (HPLC). Detection at 260 nm with a buffer solution containing 30 mM sodium borate (adjusted to pH = 10.56 with 0.05N NaOH) and acetonitrile (9 : 1) in CE or with a linear gradient elution containing 20 mM KH₂PO₄ with 0.05% phosphoric acid (pH = 2.91) and methanol in HPLC was found to be the most suitable approach for this separation. Contents of six components (2, 3, 7, 8, 9, 11) in crude Rhei Rhizoma extract could easily be determined within 39 min by CE or 63 min by HPLC. The effects of buffers on this separation and the validation of the two methods were studied.     

Liquid Chromatographic Determination of the Constituents in Shao-yao-tang and Related Chinese Herbal Preparations

A high-performance liquid chromatographic method for the separation of twenty one constituents of Shao-yao-tang including six flavonoids, six alkaloids, three anthraquinones, three carboxylic acids, one monoterpene, one saponin, and one aldehyde was developed. Detection at 275 nm with a linear gradient elution system consisting of tetrabutylammonium bromide (TBA) and acetic acid solution was found to be suitable for determination of nineteen marker substances in an unpretreated Shao-yao-tang extract within 75 min. This method can also be used to analyze 11–14 components in a number of Chinese herbal preparations such as San-huang-hsieh-hsin-tang, Ching-chieh-lien-chiao-tang, San-tsung-kuei-chien-tang, Chai-hu-ching-kan-tang, and Ching-yin-li-ke-tang.     

Consistent Petrov–Galerkin finite element simulation of channel flows

In this paper, Navier–Stokes fluid flows in curved channels are considered. Upstream of the backward‐facing step, there exists a channel with a 90° bend and a fixed curvature of 2.5. The purpose of conducting this study was to apply a finite element code to study the effect of the distorted upstream velocity profile developing over the bend on laminar expansion flows behind the step. The size of the eddies formed downstream of the step is addressed. The present work employs primitive velocities, which stagger the pressure working variable, to assure satisfaction of the inf–sup stability condition. In quadratic elements, spatial derivatives are approximated within the consistent Petrov–Galerkin finite element framework. Use of this method aids stability in the sense that artificial damping is solely added to the direction parallel to the flow direction. Through analytical testing, in conjunction with two other benchmark tests, the integrity of applying the computer code in quadratic elements is verified. Copyright © 1999 John Wiley & Sons, Ltd.