Centred TVD schemes for hyperbolic conservation laws

New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented.     

A localic theory of lower and upper integrals

An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non‐negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non‐negative upper reals, then its upper integral with respect to a covaluation and with domain of integration bounded by a compact subspace is an upper real. Spaces of valuations and of covaluations are defined. Riemann and Choquet integrals can be calculated in terms of these lower and upper integrals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of part-per-milliard concentrations of mercury by atomic- fluorescence flame spectrometry

A method is reported for the determination of mercury in the range 0.002-1 microg/ml . Mercury is extracted by dithizone from aqueous solutions into chloroform or isobutyl methyl ketone, the organic solution is aspirated into a hydrogen-oxygen name, and the intensity of atomic-fluorescence of mercury is measured. The method should be particularly useful for the determination of mercury in urine and for the determination of organic-bound mercury without prior decomposition.     

Growth and characterisation of GaN with reduced dislocation density

Two GaN MOVPE growth methods to reduce the threading dislocation (TD) density have been explored. The combined effects of (1) in situ SiN_x masking of the sapphire substrate and (2) starting the epitaxial growth at low V-to-III ratio on the GaN film quality were studied by atomic force microscopy, transmission electron microscopy and high-resolution X-ray diffraction. It was found that the annealing condition of the low-temperature nucleation layer after in situ SiN_x masking is critical in order to decrease the density of nucleation sites and hence increase the average grain size to about 5 μm. However, the coalescence of large grains with vertical side facets results in the formation of dense bundles of TDs at the grain boundaries combined with large numbers of basal-plane dislocation loops throughout the film. The formation of these dislocations can be prevented by starting the epilayer growth at low V-to-III ratio, resulting in the formation of grains with inclined side facets. The interaction of the TDs with the inclined side facets causes the dislocations to bend 90 as the grains grow in size and coalesce. GaN films with dislocation densities as low as 1×10⁸ cm⁻², giving full-width at half-maximum values of 180 and 220 arcsec for respectively (002) and (302) omega scans, were achieved by the combination of in situ masking and low V–III ratio epilayer growth. Hall carrier mobility values in excess of 900 cm² V ⁻¹ s⁻¹ were deduced for Si-doped layers.     

Junction conditions in general relativity

We examine the three sets of junction conditions commonly used in general relativity: those due to Darmois, to O'Brien and Synge, and to Lichnerowicz. We show that those due to Darmois and Lichnerowicz are equivalent. The O'Brien and Synge set is stronger than the other two and is unsatisfactory in that it may rule out physically plausible junctions. We conclude that the Darmois set is the most convenient and reliable.