Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

6(5H)-phenanthridinones. II. Preparation of substituted 6(5h)-phenanthridinones from 9-oxofluorenes

A number of 6(5H)-phenanthridinones have been conveniently prepared from 9-oxofluorenes through the Schmidt reaction. It has been found that all amino and nitro 9-oxofluorenes thus far tried gave substituted 6(5H)-phenanthridinones with the amino or nitro group situated in the benzene ring attached to the nitrogen of the lactam group. UV and IR spectral data are presented for these compounds.     

Studies on the determination of diacetyl guanfubase A concentration in rabbit plasma and pharmacokinetics

A gas chromatographic method for monitoring diacetyl guanfubase A in plasma is described. The procedure involved a single solvent extraction of drug from rabbit plasma into ethyl acetate with guanfubase A as an internal standard. The extract was analyzed subsequently on a gas chromatograph equipped with a hydrogen flame ionization detector. The recovery was 86.43% +/- 6.90% (+/- SD); the RSD of within-day and between-day was 2.81%-5.26% and 5.22%-8.24%, respectively; the regression line was linear over the concentration range of 25-200 micrograms/mL, the limit of detection was 10 micrograms/mL. No endogeneous interference was found in chromatograms of the biological samples. This method was applied to the pharmacokinetic study of diacetyl guanfubase A in rabbits.     

Chemische Vitamin D<Subscript>3</Subscript>-Bestimmung in Lebertran

The different aspects of Vitamin D₃ determination and the data reported in the literature are discussed. The spectrophotometric determination of Vitamin D₃ in cod-liver oil is carried out after the alkaline saponification, extraction of unsaponified parts, precipitation of accompanying sterols and the column- and thin-layer chromatographic purification and separation of vitamin D₃ on 40 cm plates from other vitamins. The dyestuff α-naphtholbenzein is suited well as standard substance for the better location and identification of vitamin D₃ zone on the thin-layer plate. The results obtained from the chemical method were checked through the simultaneous biological determination.     

Exposure dose assessment and discussion on radioisotope production and application

The exposure dose status on radioisotope production and application in China has been assessed in the paper. The average annual occupational exposure dose received by workers in the radioisotope production is about one tenth of the annual dose limit in normal situation. It is less than one twentieth for workers in the radioisotope applications. However, the annual collective dose for the latter is higher than the former by one oder of magnitude due to the larger number of workers in the application field. Although the output of radioisotopes increased doubly in 1980's as compared with 1970's, the increase on the annual collective dose was not obvious. For exposure to the public,¹³¹I for example, the collective dose in the radioisotope production decreased by one to two orders of magnitude and the releasing factor reduced by two orders of magnitude. Therefore, the exposure dose received by workers in radioisotope production and application is lower in normal situation. However, the facts worth paying attention to are that there were many events and accidents which happened in the radioisotope applications, especially at the irradiation facilities. The probability of fatal accident was as high as 10^–3 per irradiator year. In order to improve the radiation safety situation, it is imperative to conduct the safety assessment for irradiation facilities, to enhance management of the radioactive wastes and spent sources and to establish the experience feedback system.