Harmonic splines for geomagnetic modelling

Which features of a geomagnetic field model on the surface of the core are really necessary in order to fit, within observational error, the field observations at and above the Earth's surface? To approach this question, we define ‘roughness’ in various ways as a norm on an appropriate Hilbert space of field models which is small when the field is smooth on the core surface. Then, we calculate the model with least norm (the smoothest model) which fits the data, sources outside the core being treated as noise. Sample calculations illustrate the effects of noise, of the choice of norm and of an uneven distribution of observing stations.     

Discussion of: Experimental test of autosuspension (southard and mackintosh, 1981)

The use of a pipe-flow experiment for testing autosuspension criteria is criticized. It is argued that the proposed criterion for autosuspension is a necessary but not a sufficient condition, and that an analysis of turbidity currents can fill this gap.     

The distribution of titanium on the lunar surface

Titanium concentrations have been derived from measurements with the lunar-orbiting gamma-ray experiment on Apollo 15 and 16 by analyzing a spectral interval in which the titanium signal is relatively enhanced. Landing site soil values provide the reference for a regression curve from which Ti concentrations in 137 regions of adequate counting statistics are calculated. Among the mare regions overflown, the southern portion of Mare Tranquillitatis contains the highest Ti concentration (4.4%), Mare Serenitatis, Mare Fecunditatis, and Mare Smythii have intermediate values corresponding to low-Ti basalts, and Mare Crisium is conspicuously low in Ti (0.9%). Regional values in the western maria range from 1.1% to 4.1%, somewhat higher in the north than in the south, with the highest values seen south and west of Aristarchus. The Aristarchus Plateau appears chemically distinct from the surrounding mare. The younger western basalts mapped by the experiment do not appear to be identical to the Apollo 11 and Apollo 17 high-Ti basalts. Low-Ti basalts predominate in the observed mare regions. Highland Ti concentrations range from undetectable to 1.5% with several exceptions; accuracy is limited by the relatively large uncertainty. Highland results suggest a north-south asymmetry which is not consistent with previously reported results for Fe and Th. Comparisons with telescopic spectral reflectance studies of the maria do not show complete agreement and suggest that effects due to Fe may not have been fully removed from the reflectance data.     

Comparison of melting relationships of some plutonic and volcanic peralkaline undersaturated rocks

From previous studies and from results of melting and crystallization sequences determined for four plutonic rocks and for four glass-bearing volcanic rocks all with peralkaline chemistry, the degree of peralkalinity, ZrO₂, TiO₂, F and Cl contents of the plutonic and holocrystalline volcanic rocks can be correlated with their melting intervals. This correlation does not hold for the glassy volcanic rocks. Analyses of whole rock and coexisting glasses suggest that rapidly chilled peralkaline volcanics may behave differently from holocrystalline peralkaline rocks due to different cooling rates causing variations in the distribution of volatiles such as Cl, between liquid and solid phases of the crystallizing melt.     

Toward a unified theory of tidally-averaged estuarine salinity structure

Equations are developed for the tidally-averaged, width-averaged estuarine salinity and circulation in a rectangular estuary. Width and depth may vary along the length of the channel, as may coefficients of vertical turbulent mixing and along channel diffusion. The system is reduced to a single first-order, nonlinear, ordinary differential equation governing the section-averaged salinity. A technique for specifying the ocean boundary condition is given, and solutions are found by numerical integration. Under different assumptions for the diffusion it is possible to reproduce the few existing analytical solutions, in particular the Hansen and Rattray (1965) Central Regime solution, and Chatwin's (1976) solution. The mathematical framework allows easy comparison of the results of different channel geometries and mixing coefficients. Of particular interest is the along-channel distribution of the diffusive fraction of up-estuary salt flux. It is shown that the Hansen and Rattray solution is always diffusion-dominated near the mouth. A theory is presented for estimating the diffusion coefficient within a tidal excursion of the mouth. It is shown that the resulting rapid along-channel increase of diffusion may explain some observed patterns of salinity structure: a decrease in both stratification and along-channel salinity gradient near the mouth. The theory is applied to the Delaware Estuary and Northern San Francisco Bay, and shows reasonable agreement with observed sensitivities of salt intrusion distance to river flow.     

Crystal morphology and surface structures of orthorhombic MgSiO3 perovskite

Orthorhombic MgSiO₃ perovskite is thought to be the most abundant mineral in the mantle of the Earth. Its bulk properties have been widely studied, but many geophysical and rheological processes are also likely to depend upon its surface and grain boundary properties. As a first step towards modelling these geophysical properties, we present here an investigation of the structures and energetics of the surfaces of MgSiO₃-perovskite, employing both shell-model atomistic effective-potential simulations, and density-functional-theory (DFT) calculations. Our shell-model calculations predict the {001} surfaces to be the energetically most stable surfaces: the calculated value of the surface energy being 2.2 J/m² for the MgO-terminated surface, which is favoured over the SiO₂-terminated surface (2.7 J/m²). Also for the polar surfaces {111}, {101} and {011} the MgO-terminated surfaces are energetically more stable than the Si-terminated surfaces. In addition we report the predicted morphology of the MgSiO₃ perovskite structure, which is dominated by the energetically most stable {001} and {110} surfaces, and which appears to agree well with the shape of grown single crystals.     

FLAIR observations of planetary nebulae in the Large Magellanic Cloud

This paper presents new observations of 97 planetary nebulae in the Large Magellanic Cloud (LMC) obtained using the FLAIR system on the UK 1.2-m Schmidt Telescope. These nebulae are mostly at the fainter end of the known population, and about 75 per cent have not been observed before in spectroscopic mode. Radial velocities have been measured using cross-correlation techniques, and represent an increase of 66 per cent in the sample of LMC planetary nebulae with known radial velocities. The major line ratios are given, and are analysed in conjunction with published data. One-quarter of the faint nebulae are Type I objects with very strong [N II ] and [S II ] lines; most of the other faint nebulae have low density, low excitation and relatively strong [S II ] lines.     

The Durham/UKST Galaxy Redshift Survey – IV. Redshift-space distortions in the two-point correlation function

We have investigated the redshift-space distortions in the optically selected Durham/UKST Galaxy Redshift Survey using the two-point galaxy correlation function perpendicular and parallel to the observer's line of sight, ξ(σ, π). On small, non-linear scales we observe an elongation of the constant ξ(σ, π) contours in the line-of-sight direction. This is a result of the galaxy velocity dispersion and is the common 'Finger of God' effect seen in redshift surveys. Our result for the one-dimensional pairwise rms velocity dispersion is 〈 w ²〉^1/2=416±36 km s⁻¹, which is consistent with those from recent redshift surveys and canonical values, but inconsistent with SCDM or LCDM models. On larger, linear scales we observe a compression of the ξ(σ, π) contours in the line-of-sight direction. This is caused by the infall of galaxies into overdense regions, and the Durham/UKST data favours a value of (Ω^0.6/ b )∼0.5, where Ω is the mean mass density of the Universe and b is the linear bias factor that relates the galaxy and mass distributions. Comparison with other optical estimates yields consistent results, with the conclusion that the data do not favour an unbiased critical-density universe.     

Modelling of the thermal dependence of structural and elastic properties of calcite, CaCO3

A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO₃; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10^?6K^?1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10^?4K^?1 is obtained.