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.     

Bioaccumulation and excretion of arsenic compounds by a marine unicellular alga,polyphysa peniculus

Polyphysa peniculus was grown in artificial seawater in the presence of arsenate, arsenite, monomethylarsonate and dimethylarsinic acid. The separation and identification of some of the arsenic species produced in the cells as well as in the growth medium were achieved by using hydride generation–gas chromatography–atomic absorption spectrometry methodology. Arsenite and dimethylarsinate were detected following incubation with arsenate. When the alga was treated with arsenite, dimethylarsinate was the major metabolite in the cells and in the growth medium; trace amounts of monomethylarsonate were also detected in the cells. With monomethylarsonate as a substrate, the metabolite is dimethylarsinate. Polyphysa peniculus did not metabolize dimethylarsinic acid when it was used as a substrate. Significant amounts of more complex arsenic species, such as arsenosungars, were not observed in the cells or medium on the evidence of flow injection–microwave digestion–hydride generation–atomic absorption spectrometry methodology. Transfer of the exposed cells to fresh medium caused release of most cell–associated arsenicals to the surrounding environment.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

氘－氚聚变等离子体中高能α粒子的诊断

本文对于用电荷交换方法或低杂波涨落的方法测量高能α粒子作了简短的评述，建议用核反应１３Ｃ（α，ｎ）１６Ｏ测量氘－氚聚变等离子体中的高能α粒子，并提出了一种减少杂质污染，增加穿透深度的方法。     

Formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber blends: Effects of preparation method,composition, and thermal condition

The effects of preparation method, composition, and thermal condition on formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber (iPP/EPR) blends were studied using modulated differential scanning calorimeter (MDSC), wide angle X‐ray diffraction (WAXD), and phase contrast microscopy (PCM). It was found that the α‐iPP and β‐iPP can simultaneity form in the melt‐blended samples, whereas only α‐iPP exists in the solution‐blended samples. The results show that the formation of β‐iPP in the melt‐blended samples is related to the crystallization temperature and the β‐iPP generally diminishes and finally vanishes when the crystallization temperature moves far from 125 °C. The phenomena that the lower critical temperature of β‐iPP in iPP/EPR obviously increases to 114 °C and the upper critical temperature decreases to 134 °C indicate the narrowing of temperature interval, facilitating the formation of β‐iPP in iPP/EPR. Furthermore, it was found that the amount of β‐iPP in melt‐blended iPP/EPR samples is dependent on the composition and the maximum amount of β‐iPP formed when the composition of iPP/EPR blends is 85:15 in weight. The results through examining the effect of annealing for iPP/EPR samples at melt state indicate that this annealing may eliminate the susceptibility to β‐crystallization of iPP. However, only α‐iPP can be observed in solution‐blended samples subjected to annealing for different time. The PCM images demonstrate that an obvious phase‐separation happens in both melt‐blended and solution‐blended iPP/EPR samples, implying that compared with the disperse degree of EPR in iPP, the preparation method plays a dominant role in formation of β‐iPP. It is suggested that the origin of formation of β‐iPP results from the thermomechanical history of the EPR component in iPP/EPR. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1704–1712, 2007     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Operator‐splitting method for the analysis of cavitation in liquid‐lubricated herringbone grooved journal bearings

This paper presents an operator‐splitting method (OSM) for the solution of the universal Reynolds equation. Jakobsson–Floberg–Olsson (JFO) pressure conditions are used to study cavitation in liquid‐lubricated journal bearings. The shear flow component of the oil film is first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component is computed by the Galerkin finite element method. Present OSM solutions for slider bearings are in good agreement with available analytical and experimental results. OSM is then applied to herringbone grooved journal bearings. The film pressure, cavitation areas, load capacity and attitude angle are obtained with JFO pressure conditions. The calculated load capacities are in agreement with available experimental data. However, a detailed comparison of the present results with those predicted using Reynolds pressure conditions shows some differences. The numerical results showed that the load capacity and the critical mass of the journal (linear stability indicator) are higher and the attitude angle is lower than those predicted by Reynolds pressure conditions for cases of high eccentricities. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.