The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

The frequency of binaries with a degenerate component

The frequency of binaries with degenerate secondary components was evaluated according to the spectral types of the primaries. It appears that this proportion is 25% for binaries with giant primary components, and less than about 17% for dwarfs.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

Nuclear reactions on accreting neutron star surface

The production of X-rays and gamma-rays in bursts is believed to be due to the rapid burning of matter accreted onto a neutron star surface from its companion, most probably a giant star. The accreted matter consists mainly of hydrogen and helium and a very small amount of heavy elements. Due to the infall of matter, the temperature at the bottom layers is raised to a value of the order of 10⁸ K. The neutron star surface density is>10⁷ g cm^–3. As hydrogen burning is a slow process under any temperature and density conditions, we consider the helium-burning reactions as the source of gamma-rays in the neutron star surface. Under high-density conditions the ordinary laboratory reaction rates should become modified. At high-density conditions, the strong screening effect due to the polarising cloud of electrons around the ions become important and enhances the reaction rates considerably. The helium-burning reactions are calculated under such conditions. The abundances of helium-burning products such as¹²C, 1¹⁶O, and²⁰Ne, etc., are computed. Under high-density and temperature conditions carbon is found to be more abundant than oxygen. Neon is completely absent in almost all the relevant physical conditions in which a strong screening effect is operative. It is suggested that explosive burning of accreted helium of 10^–13 M will account for the observed energy of gamm-ray burst.     

Further analysis of temperature and emission measure during the decay phase of solar flares derived from soft X-ray light curves

The light curves of soft X-ray lines, observed by the Flat Crystal Spectrometer on Solar Maximum Mission during eight solar flares are modeled to determine the plasma temperature and emission measure as functions of time using the method first presented by Bornmann (1985, Paper I), but modified to include a ² search routine. With this modification the technique becomes more general, more accurate, and applicable throughout the gradual phase of the flare. The model reproduces the light curves of the soft X-ray lines throughout these flares. Model fits were repeated for each flare using five different sets of published line emissivity calculations. The emissivities of Mewe and Gronenschild (1981) consistenly gave the best fits to the observed light curves for each flare.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

Relationship between footwall composition,crustal contamination,and fluid–rock interaction in the Platreef,Bushveld Complex,South Africa

In the northern limb of the 2.06-Ga Bushveld Complex, the Platreef is a platinum group elements (PGE)-, Cu-, and Ni-mineralized zone of pyroxenite that developed at the intrusion margin. From north to south, the footwall rocks of the Platreef change from Archaean granite to dolomite, hornfels, and quartzite. Where the footwall is granite, the Sr-isotope system is more strongly perturbed than where the footwall is Sr-poor dolomite, in which samples show an approximate isochron relationship. The Nd-isotope system for samples of pyroxenite and hanging wall norite shows an approximate isochron relationship with an implied age of 2.17 ± 0.2 Ga and initial Nd-isotope ratio of 0.5095. Assuming an age of 2.06 Ga, the ɛNd values range from −6.2 to −9.6 (ave. −7.8, n = 17) and on average are slightly more negative than the Main Zone of the Bushveld. These data are consistent with local contamination of an already contaminated magma of Main Zone composition. The similarity in isotope composition between the Platreef pyroxenites and the hanging wall norites suggests a common origin. Where the country rock is dolomite, the Platreef has generally higher plagioclase and pyroxene δ ¹⁸O values, and this indicates assimilation of the immediate footwall. Throughout the Platreef, there is considerable petrographic evidence for sub-solidus interaction with fluids, and the Δ _{plagioclase–pyroxene} values range from −2 to +6, which indicates interaction at both high and low temperatures. Whole-rock and mineral δD values suggest that the Platreef interacted with both magmatic and meteoric water, and the lack of disturbance to the Sr-isotope system suggests that fluid–rock interaction took place soon after emplacement. Where the footwall is granite, less negative δD values suggest a greater involvement of meteoric water. Consistently higher values of Δ _{plagioclase–pyroxene} in the Platreef pyroxenites and hanging wall norites in contact with dolomite suggest prolonged interaction with CO₂-rich fluid derived from decarbonation of the footwall rocks. The overprint of post crystallization fluid–rock interaction is the probable cause of the previously documented lack of correlation between PGE and sulfide content on the small scale. The Platreef in contact with dolomite is the focus of the highest PGE grades, and this suggests that dolomite contamination played a role in PGE concentration and deposition, but the exact link remains obscure. It is a possibility that the CO₂ produced by decarbonation of assimilated dolomite enhanced the process of PGE scavenging by sulfide precipitation.     

Asymmetrically zoned reaction rims: assessment of grain boundary diffusivities and growth rates related to natural diffusion-controlled mineral reactions

This study explores garnet coronas around hedenbergite, which were formed by the reaction plagioclase + hedenbergite→garnet + quartz, to derive information about diffusion paths that allowed for material redistribution during reaction progress. Whereas quartz forms disconnected single grains along the garnet/hedenbergite boundaries, garnet forms ～20‐μm‐wide continuous polycrystalline rims along former plagioclase/hedenbergite phase boundaries. Individual garnet crystals are separated by low‐angle grain boundaries, which commonly form a direct link between the reaction interfaces of the plagioclase|garnet|hedenbergite succession. Compositional variations in garnet involve: (i) an overall asymmetric compositional zoning in Ca, Fe²⁺, Fe³⁺ and Al across the garnet layer; and (ii) micron‐scale compositional variations in the near‐grain boundary regions and along plagioclase/garnet phase boundaries. These compositional variations formed during garnet rim growth. Thereby, transfer of the chemical components occurred by a combination of fast‐path diffusion along grain boundaries within the garnet rim, slow diffusion through the interior of the garnet grains, and by fast diffusion along the garnet/plagioclase and the garnet/hedenbergite phase boundaries. Numerical simulation indicates that diffusion of Ca, Al and Fe²⁺ occurred about three to four, four and six to seven orders of magnitude faster along the grain boundaries than through the interior of the garnet grains. Fast‐path diffusion along grain boundaries contributed substantially to the bulk material transfer across the growing garnet rim. Despite the contribution of fast‐path diffusion, bulk diffusion through the garnet rim was too slow to allow for chemical equilibration of the phases involved in garnet rim formation even on a micrometre scale. Based on published garnet volume diffusion data the growth interval of a 20‐μm‐wide garnet rim is estimated at ～10³–10⁴ years at the inferred reaction conditions of 760 ± 50 °C at 7.6 kbar. Using the same parameterization of the growth law, 100‐μm‐ and 1‐mm‐thick garnet rims would grow within 10⁵–10⁶ and 10⁶–10⁷ years respectively.     

The role of heterogeneous strain in the development and preservation of a polymetamorphic record in high-P granulites, western Canadian Shield

Mafic rocks in the Chipman domain of the Athabasca granulite terrane, western Canadian Shield, provide the first well‐documented record of two distinct high‐P granulite facies events in the same domain in this region. Textural relations and the results of petrological modelling (NCFMASHT system) of mafic granulites are interpreted in terms of a three‐stage tectonometamorphic history. Stage 1 involved development of the assemblage Grt + Cpx + Qtz ± Pl (M₁) from a primary Opx‐bearing igneous precursor at conditions of 1.3 GPa, 850–900 °C. Field and microstructural observations suggest that M₁ developed synchronously with an early S₁ gneissic fabric. Stage 2 is characterized by heterogeneous deformation (D₂) and synkinematic partial retrogression of the peak assemblage to an amphibole‐bearing assemblage (M₂). Stage 3 involved a third phase of deformation and a return to granulite facies conditions marked by the prograde breakdown of amphibole (Amph₂) to produce matrix garnet (Grt_3a) and the coronitic assemblage Cpx_3b + Opx_3b + Ilm_3b + Pl_3b (M_3b) at 1.0 GPa, 800–900 °C. M₁ and M_3b are correlated with 2.55 and 1.9 Ga metamorphic generations of zircon, respectively, which were dated in a separate study. Heterogeneous strain played a crucial role in both the development and preservation of these rare examples of multiple granulite facies events within single samples. Without this fortuitous set of circumstances, the apparent reaction history could have incorrectly led to an interpretation involving a single‐cycle high‐grade event. The detailed P–T–t–D history constructed for these rocks provides the best evidence to date that much of the east Lake Athabasca region experienced long‐term lower crustal residence from 2.55 to 1.9 Ga, and thus the region represents a rare window into the reactivation and ultimate stabilization processes of cratonic lithosphere.     

Impact evaluation on groundwater of the infiltration of an urban wastewater geopurification system placed over a detrital aquifer in a semiarid region (Spain)

Over a period of 4 years and 4 months, the geopurification installations at Dehesas de Guadix (Granada, Spain) were monitored to determine the impact on soil and groundwater of the controlled discharge of urban wastewater, and also to identify the best indicators of the entry of the recharged water into the aquifer. The installations are located in an area where the climate is Mediterranean sub-arid, with an average precipitation of less than 287 mm/year, and a rate of evapotranspiration that is almost three times greater. The system was controlled by determining the balance of majority nutrients and boron in the soil and in the groundwater, both at the points affected directly by the wastewater discharge and at others. The quantity of mass discharged was relatively large (COD 14,656 g/m², NO₃ 85 g/m², NO₂ 4 g/m², NH₄ 2,425 g/m², PO₄ 1,143 g/m², K 1,531 g/m², B 63 g/m²). It was observed that the elimination of nutrients within the soil (COD 97.5%, PO₄ 94.4%, K 59.17%, N _total 18.8%, B 12.69%) was very efficient except for the nitrogen, which nevertheless did not reach the groundwater, as it was eliminated at deep levels of the unsaturated zone. Only 12.69% of the boron was removed, and appreciable, increasing amounts of this element did reach the groundwater. Unexpectedly, none of the majority nutrients behaved as a reliable indicator of the impact on groundwater; despite this, the boron and the bicarbonate did clearly reflect the arrival of the recharged water, and are proposed as the best indicators.     

Bedrock, soils, and hillslope hydrology in the Central Texas Hill Country, USA: implications on environmental management in a carbonate-rock terrain

The Hill Country of Central Texas, USA, is undergoing rapid socioeconomic development, but environmental management of this region is hampered by misconceptions about local bedrock, soils, terrain, and hydrologic processes. The Hill Country is underlain mostly by Glen Rose Limestone (Lower Cretaceous) and exhibits a stepped terrain, which has been incorrectly attributed to alternating hard and soft bedrock strata. Other characteristics mistakenly attributed to this landscape include thin soils with scant water-retention capabilities, and rapid runoff as the dominant hydrologic process. This report presents new findings: unweathered bedrock is well indurated, but interbeds exhibit variable weathering rates. Recessive slopes (“risers”) on this stepped terrain result from rapid deterioration of strata having generally heterogeneous depositional fabrics (bioturbation and irregular clay partings) in contrast to ledge-forming strata having homogeneous fabrics. A stony regolith is thus formed beneath risers, providing porous and permeable ground that retards runoff and promotes the formation of moderately deep to deep (two-tiered) regolith/soil zones. These surficial materials on local steep slopes compose important natural environmental buffers; they support diverse biota and enhanced geochemical cycling of nutrients; they also exhibit significant water retention and enhanced erosion abatement. Proper land management demands recognition of these attributes in the siting, design, and construction of facilities.