The deformation and compaction of partial molten zones

Summary. The segregation of melt from a partially molten source region requires a corresponding deformation of the unmelted residue ('matrix'). The role of matrix deformation during melt segregation is examined using simple one-dimensional models, for which the deformation consists only of bulk compression or 'compaction'. In model I, a volume fraction φ₀ of ascending mantle material undergoes pressure-release melting at a depth z = 0 (localized melting). Compaction of the matrix occurs in a boundary layer whose thickness (reduced compaction length δ_R) is proportional to the square root of the matrix viscosity. In the Earth's mantle, δ_R∼ 10–100 m, indicating that compaction cannot be important over large distances. Model II examines the case in which melting occurs over a depth range of order h (distributed melting). In the limit h ≪δ_R, the solution is the same as for the case of localized melting, except in a 'melting layer' of thickness ∼ h near z = 0. In the more realistic limit h ≫δ_R, compaction makes a negligible contribution to the balance of forces associated with melt segregation. This result is also valid for the more general case of two-dimensional flow. Compaction is therefore likely to be of negligible importance in the Earth's mantle, with the consequence that melt segregation can be accurately described by Darcy's law.     

An easy-to-use Model for the Optical Thickness and Ambient Illumination within Cometary Dust Comae

We define a procedure which allows estimation of the optical thickness of a cometarydust coma and the ambient illumination of the nucleus for any given comet, if estimatesof the nucleus radius and the dust activity (Afρ) are available. The calculation isperformed for a singly scattering coma with a cos(ϑ) distribution of dust overits day side. We find that the ambient illumination is of the same order as the incidentsunlight if the optical thickness is of order one. The optical thickness increases, all elseequal, linearly with the nucleus radius. Therefore the effect of the presence of the comamay be neglected for small (≈ 1 km diameter) comets, but is important forcomets such as 1P/Halley and Hale–Bopp.     

The geologist's dilemma: predicting the future behaviour of buried radioactive wastes

The last 10–15 years have produced a considerable amount of research into the geological disposal of radioactive wastes. This has had some very beneficial spin-offs for the geosciences. There are, however, a number of areas where it is difficult for earth scientists to provide quantitative information required for the types of long-term safety assessment being performed at present. With the likely increased stringency with which we may begin to treat other industrial wastes, much is to be learned from the radioactive waste experience. This article reviews some of the geological issues in constraining long-term predictions, discusses how geological data are used, and questions exactly what it is that we are trying to achieve in the management of these wastes and in the regulations concerning their disposal.     

The temperatures of dust-enshrouded active galactic nuclei

A high density of massive dark objects (MDOs), probably supermassive black holes, in the centres of nearby galaxies has been inferred from recent observations. There are various indications that much of the accretion responsible for producing these objects took place in dust-enshrouded active galactic nuclei (AGNs). If so, then measurements of the intensity of background radiation and the source counts in the far-infrared and submillimetre wavebands constrain the temperature of dust in these AGNs. An additional constraint comes from the hard X-ray background, if this is produced by accretion. One possibility is that the dust shrouds surrounding the accreting AGNs are cold, about 30 K. In this event, the dusty AGNs could be some subset of the population of luminous distant sources discovered at 850 μm using the SCUBA array on the James Clerk Maxwell Telescope, as proposed by Almaini, Lawrence & Boyle. An alternative is that the dust shrouds surrounding the accreting AGNs are much hotter (>60 K). These values are closer to the dust temperatures of a number of well-studied low-redshift ultraluminous galaxies that are thought to derive their power from accretion. If the local MDO density is close to the maximum permitted, then cold sources cannot produce this density without the submillimetre background being overproduced if they accrete at high radiative efficiency, and thus a hot population is required. If the dust-enshrouded accretion occurred at similar redshifts to that taking place in unobscured optical quasars, then a significant fraction of the far-infrared background radiation measured by COBE at 140 μm, but very little of the submillimetre background at 850 μm, may have been produced by hot dust-enshrouded AGNs which may have already been seen in recent Chandra X-ray surveys.     

On a generalization of Filon's method and the computation of the oscillatory integrals of seismology

Summary. We review Filon's method (FM) for the quadrature of oscillatory integrals and then introduce a generalization of Filon's method (the GFM) which enables us to treat a large class of oscillatory integrals to which FM cannot be directly applied. One member of this class is the integral ( p ) exp [ sg ( p )] dp which occurs in the spectral WKBJ and Cagniard-de Hoop methods of seismogram synthesis. Another large class of integrals can be treated directly with FM but is better treated with the GFM since, for a given error tolerance, the GFM is simpler and faster. This class consists of integrals of the form ( p ) J ( s, p ) dp in which J ( s, p ) is a special function with an asymptotic expansion valid for large s. Such integrals occur in the reflectivity method. In general, every non-Filon formula for the quadrature of integrals from either class has an associated GFM formula (called the GFM analogue) which reduces to the original formula as s approaches zero but is more efficient than the original formula wher, s is large. We show how the GFM can be applied to the computation of synthetic seismograms in the reflectivity method and the spectral WKBJ method.
Although reflectivity integrals can, in theory, be computed with FM the GFM is easier to code and more economical. For reflectivity computations where: (a) the source and receiver are many wavelengths apart, or (b) the depth to the reflectivity zone is much greater than its thickness, the GFM approach is much more efficient than any non-Filon quadrature technique. Some test calculations are presented for wavefields containing only body waves and for wavefields containing both body waves and locked modes.
In the spectral WKBJ method the GFM permits the use of a much greater step size in the quadrature than would otherwise be possible. Each quadrature step contains a stationary point so no advantages accrue from deforming the contour of integration over the saddle points of the integrand.     

Simulations of the sun's polar magnetic fields during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have simulated the evolution of the radial component of the solar photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the line-of-sight polar fields as seen from Earth. The observed timing and strength of the polar-field reversal during cycle 21 can be accounted for by supergranular diffusion alone, for a diffusion coefficient of 800 km² s^-1. For an assumed 300 km² s^-1 rate of diffusion, on the other hand, a poleward meridional flow with a moderately broad profile and a peak speed of 10 m s^-1 reached at about 5° latitude is required to obtain agreement between the simulated and observed fields. Such a flow accelerates the transport of following-polarity flux to the polar caps, but also inhibits the diffusion of leading-polarity flux across the equator. For flows faster than about 10 m s^-1 the latter effect dominates, and the simulated polar fields reverse increasingly later and more weakly than the observed fields.Laboratory for Computational Physics and Fluid Dynamics.E. O. Hulburt Center for Space Research.     

Major ion variation and efflux related to discharge in a mafic piedmont province watershed

Major-ion variability related to discharge was analysed in a forested 187 km² mafic Piedmont Province watershed using statistical (both parametric and non-parametric), graphical (box-plots) and curve-fitting (log concentration-log discharge) techniques. Baseflow alkalinity and base cation concentrations show systematic temporal variations as a result of the influx of additional water that occurs during the late autumn to early spring. Regression analyses indicate that storm-related discharge and baseflow generated during periods of water surplus are characterized by similar dilution slopes. Mass balance estimates indicate that the additional water, which comprises storm/recession discharge and base-flow from late autumn to early spring, is between about 30 and 80% as concentrated as summer low-flow. The thick clay-rich soil mantle represents a key control on solute concentrations in that it stores water for periods of time sufficient for a high degree of water-mineral interaction to occur. Hence solute-discharge relationships (C = aQ^b, where b is typically < 0) are characterized by relatively low slope values and there is ample acid neutralizing capacity throughout the range of discharge. Owing to the predominance of amphibolite, solute efflux related to rock weathering from the Falling Creek watershed is much greater than other more felsic locations within the region. Statistical analyses (Mest and the non-parametric Mann-Whitney-Wilcoxon test), along with accompanying box-plot representations, provide a useful method of describing systematic annual hydrochemical variation within streamflow. These methods are particularly effective for those instances in which a long-term data set exists, but is limited to relatively few sampling periods per year.     

Distance measurements as a probe of cosmic acceleration

A major recent development in observational cosmology has been an accurate measurement of the luminosity distance–redshift relation out to redshifts z =0.8 from Type Ia supernova standard candles. The results have been argued as evidence for cosmic acceleration. It is well known that this assertion depends on the assumption that we know the equation of state for all mass–energy other than normal pressureless matter; popular models are based either on the cosmological constant or on the more general quintessence formulation. However, this assertion also depends on a number of other assumptions, implicit in the derivation of the standard cosmological field equations: large-scale isotropy and homogeneity, the flatness of the Universe, and the validity of general relativity on cosmological scales (where it has not been tested). A detailed examination of the effects of these assumptions on the interplay between the luminosity distance–redshift relation and the acceleration of the Universe is not possible unless one can define the precise nature of the failure of any particular assumption. However a simple quantitative investigation is possible and reveals a number of considerations about the relative importance of the different assumptions. In this paper we present such an investigation. We find that the relationship between the distant-redshift relation and the sign of the deceleration parameter is fairly robust and is unaffected if only one of the assumptions that we investigate is invalid so long as the deceleration parameter is not close to zero (it would not be close to zero in the currently favoured Ω_Λ=1−Ω_matter=0.7 or 0.8 Universe, for example). Failures of two or more assumptions in concordance may have stronger effects.