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.     

A remark on Mansfield's imprimitivity theorem

We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).

     

Persulphate initiated polymerisation of methacrylamide—I: Kinetics and molecular weight dependences

A kinetic study of the aqueous persulphate initiated polymerisation of methacrylamide has shown that the rate of polymerisation is represented by the equation $\text{R}{}_{\mathrm{p}}\text{= k [}\text{M}\text{] [}\text{I}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ where the overall rate constant, $\text{k = 1.3 × 10}{}^9\text{exp}\text{(?18,400/}\text{RT}\text{) 1}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{s}{}^{\mathrm{?1}}$. Chain transfer with monomer, where C_M = 5.4 × 10^?3 at 60°, is shown to be the dominant transfer step. Comparison with kinetic studies of the analogous acrylamide polymerisation shed doubt on the ‘cage effect’ interpretation of complex orders with respect to monomer. An alternative explanation is proposed.     

Gas chromatographic-mass spectrometric analysis of acids and phenols in distilled alcohol beverages. Application of anion-exchange disk extraction combined with in-vial elution and silylation

A GC-MS protocol for profiling spirits, based on 19 acids and phenolic compounds, has been proposed and evaluated. The method combined a simple preconcentration procedure based on solid-phase (anion-exchange) disk extraction, and in-vial elution and silylation of the analytes. The derivatized extract was directly injected into the GC-MS system. These analytes were: C6, C8, C10, C12 acids, pyruvic acid, 2-furoic acid, succinic acid, fumaric acid, glutaric acid, lactic acid, glycolic acid, malic acid, tartaric acid, citric acid, vanillin, syringaldehyde, coniferaldehyde, vanillic acid and gallic acid. The profiles of six different spirits were found reproducible from day-to-day with <20% RSD for measurements of most of the analytes at different concentrations. Recoveries of individual analytes appear to be affected by the level of tannins in the spirits, and they varied from sample to sample. The method of standard addition was used to quantify age-related analytes. Good linearity of response with correlation coefficients in the range of 0.992-0.999 was obtained. The results of the study indicate that for spirits of the same brand but of different ages, the amounts of these analytes appear to increase with the ageing period.     

Coordination complexes of acetylenic phosphines and diphosphines

The reactions of π-cyclopentadienylnickel carbonyl dimer with 3,3,3-trimethylpropynyldiphenylphosphine and phenylethynyldiphenylphosphine are described. The products have been characterized by elemental and mass spectral analysis, infrared and NMR spectroscopy. An acetylene bridged complex (π-C₅H₅Ni)₂Ph₂PC₂-t-Bu, containing an uncoordinated phosphorus atom, has been prepared. The complex can be oxidized to the phosphine oxide derivative (π-C₅H₅Ni)₂Ph₂P(O)C₂-t-Bu and converted to the phosphonium salts with methyl iodide or ethyl bromide. These are the first reported π-complexes of phosphonium salts. The complex (π-C₅H₅Ni)₂Ph₂PC₂-t-Bu forms the novel mixed metal derivative [PdCl₂][(π-C₅H₅Ni)₂Ph₂PC₂-t-Bu]₂ from bis(benzonitrile)-palladium dichloride. The dicarbonyl complexes Ni(CO)₂(Ph₂PC₂R)₂ (R  t-Bu, Ph), the phosphine oxide complex (π-C₅H₅Ni)₂(Ph₂P(O)C₂Ph) and the trinuclear nickel carbonyl derivative Ni(CO)₃[(π-C₅H₅Ni)₂Ph₂PC₂Ph] are described.     

Experimental measurement and prediction of hydrate forming conditions in the nitrogen-propane-water system

Experimental data on initial hydrate formation conditions have been obtained for the nitrogen-propane-water system in the L₁HG, L₁L₂H, and L₁L₂HG regions, where L₁ is the water rich liquid phase, L₂ is the hydrocarbon rich liquid phase, H is the hydrate and the G is the vapor phase. The measurements covered a range of temperatures from about 275 to 293 K and pressures from about 0.3 to 17.0 MPa. The concentrations covered for the L₁HG region extended from 0.94 to 75.0 mole percent propane in the gas phase, and for the L₁L₂H region they extended from 83.1 to 99.0 mole percent in the condensed liquid phase. Four-phase measurements were made at concentrations of propane from 18.1 to 71.1 mole percent in the gas phase.The experimental data were used to find a fitted binary interaction parameter for predicting hydrate formation in systems containing nitrogen and propane.     

A simple reliable approximation for isotropic intermolecular forces. A critical test using HH(3Σu+) as a model

A simple semi-empirical approximation for the exchange energy (E_x), coupled with a tractable representation of the Coulomb energy (E_C), has been found to yield very accurate results for the isotropic part of the interaction energy (E_int = E_x + E_C) between two closed shell systems. The expression for E_int is based on the knowledge of the first order Coulomb energy and the first three terms in the asymptotic long range expansion of the second order Coulomb energy for the interaction and contains but one adjustable parameter which occurs in E_x. The usefulness of this approach for evaluating E_int is tested critically by using the non-bonded H(1s)H(1s) (³Σ_u⁺) interaction as a model (accurate values of the total interaction energy, the exchange energy, and various orders of Coulomb energies, are available for a wide range of R for this system). The results obtained for both E_int and (dE_int/dR) are inremarkable agreement with the exact results of Kotos and Wolniewicz for R > 3 a_o. Since the law of corresponding states for inert gas pairs holds equally well for the HH(³Σ_u⁺) interaction, our analysis of this simple system yields valuable information on the reliability of the approach for other van der Waals dimers.     

Laser cladding of copper with molybdenum for wear resistance enhancement in electrical contacts

Laser cladding of Mo on Cu has been attempted with the aim of enhancing the wear resistance and hence increasing the service life of electrical contacts made of Cu. In order to overcome the difficulties arising from the large difference in thermal properties and the low mutual solubility between Cu and Mo, Ni was introduced as an intermediate layer between Mo and Cu. The Ni and Mo layers were laser clad one after the other to form a sandwich layer of Mo/Ni/Cu. Excellent bonding between the clad layer and the Cu substrate was ensured by strong metallurgical bonding. The hardness of the surface of the clad layer is seven times higher than that of the Cu substrate. Pin-on-disc wear tests consistently showed that the abrasive wear resistance of the clad layer was also improved by a factor of seven as compared with untreated Cu substrate. The specific electrical contact resistance of the clad surface was about 5.6 × 10⁻⁷ Ω cm².     

Application of spectroscopic imaging in epilepsy

Functional and anatomical neuroimaging has had a dramatic effect on the evaluation of patients for seizure surgery. The demonstration by PET that the epileptogenic focus has interictal metabolic abnormalities has allowed a greater number of patients to come to seizure surgery, with fewer of these patients requiring intracranial electrode evaluations. Metabolic changes have also been demonstrated utilizing single voxel and whole brain ¹H and ³¹P MRS imaging techniques with the interictal focus characterized by increased Pi, pH, and decreased PME and NAA. These findings can be used to accurately lateralize temporal lobe as well as frontal lobe epilepsy. Furthermore, there is evidence that these findings can be used to localize the seizure focus with the changes specific for the epileptogenic region; although, more diffuse changes both ipsilaterally and contralaterally have been seen. In patients with anterior hippocampal seizure foci the pH is significantly alkaline only in the ipsilateral hippocampus, whereas the increased Pi and decreased PME can be seen throughout the ipsilateral temporal lobe. When compared to controls the contralateral hemisphere is acidotic. Decreased NAA concentrations as well as NAA/Cr ratios have been demonstrated in the epileptogenic region in temporal and frontal lobe epilepsy. The decreased NAA has been correlated with the severity of cell loss, and may be a more sensitive measure than qualitative or quantitative measures of the hippocampal atrophy; however, the NAA decrease is more widespread than just the epileptogenic focus but may be maximal at the site of seizure initiation. In preliminary work, NAA maps of deviation from normality have suggested the maximal change to coincide with the epileptogenic region. These results suggest that in focal epilepsy there is abnormal metabolic activity throughout the brain detectable by MRS, with patterns of metabolic asymmetry that are useful for seizure localization.