The Cartesian method for solving partial differential equations in spherical geometry

Cartesian coordinates are used to solve the nonlinear shallow-water equations on the sphere. The two-dimensional equations, in spherical coordinates, are first embedded in a three-dimensional system in a manner that preserves solutions of the two-dimensional system. That is, solutions of the three-dimensional system, with appropriate initial conditions, also solve the two-dimensional system on the surface of the sphere. The higher dimensional system is then transformed to Cartesian coordinates. Computations are limited to the surface of the sphere by projecting the equations, gradients, and solution onto the surface. The projected gradients are approximated by a weighted sum of function values on a neighboring stencil. The weights are determined by collocation using the spherical harmonics in trivariate polynomial form. That is, the weights are computed from the requirement that the projected gradients are near exact for a small set of spherical harmonics. The method is applicable to any distribution of points and two test cases are implemented on an icosahedral geodesic grid. The method is both vectorizable and parallelizable.     

Plagioclase—melt equilibria

The crystallization of plagioclase feldspar from magmatic liquid has been investigated experimentally under equilibrium conditions at 1 atm total pressure in the temperature range 1400-1095°C. Natural and synthetic melts of composition basalt to rhyolite were used, crystallizing plagioclase of composition An₈₉-An₃₂.The experimental results are analyzed initially in terms of elemental plagioclase/melt partition coefficients (D). D_Si is always less than unity and is invariant with temperature. D_A1 is always greater than unity and is relatively insensitive to temperature. D_Na is less than unity above 1200°C and is strongly dependent upon temperature. D_Ca is greater than unity below 1430°C and is strongly dependent upon temperature.Analysis of the temperature-dependence of equilibrium constants for plagioclase-melt formation and exchange reactions in which several mixing models for the melt are considered, leads to the conclusion that, with appropriate choice of melt-components, the melt-components mix quasi-ideally. At fixed temperature in the absence of H₂O, the equilibrium constant for the equilibrium of albite with the melt is insensitive to changes in melt-composition, and is insensitive to changes in pressure up to at least 10 kbars. As a consequence the composition of plagioclase crystallizing at known temperature and at low total pressure from a dry melt of known composition may be predicted []. However, the equilibrium constant is sensitive to changes in water pressure.The analysis further suggests that Na is intimately associated with tetrahedrally-coordinated Al in the melt, while Ca appears to be partitioned between at least two distinct melt-sites.     

Chronology of cenozoic igneous and tectonic events in the central Chilean Andes — latitudes 35° 30′ to 36°S

Sixty-six K---Ar dates from igneous rocks in the central Chilean Andes between 33° and 38°S are reported in this study. From these results and observed field relations, major Cenozoic volcanic and intrusive rock units are divided into chronologic groups representing igneous events.Volcanic units of Oligocene (33.3–27.9 m.y.) and Early Miocene (20.2 m.y.) age have been dated west of the present range at 33°S but neither the magnitude nor extent of these volcanic events has yet been established. Extensive Middle to Late Miocene volcanism (15.3–6.4 m.y.) followed by regional folding is recognized in the map area between 35° 20′ and 36°S. Partly contemporaneous Middle Miocene volcanism (18.4–13.7 m.y.) also followed by regional folding is recorded in the Andes between 37° 30′ and 38°S. General volcanic quiescence from 6.4 to 2.5 m.y. is observed in the map area but whether this volcanic hiatus is of regional significance is not known.The majority of the K---Ar dates document a history of nearly continuous volcanism throughout the last 2.5 m.y. in the map area. The abundant and diverse sequences of volcanic strata formed during this time, have been divided into four successive age groups which as map units show the evolution and distribution of latest volcanic activity.Landforms preserved by this volcanic series show that topographic relief similar to the present has prevailed during this time. Deep incision of rivers into young volcanic terrain, estimated to be on the order of 1–2 m/1000 years, has produced a complex volcanic and morphologic record.Four plutons dated in this study give ages of 62.0, 41.3, 19.5, and 7.0 m.y. No spatial pattern of emplacement is observed in the map area where three of these plutons are represented.Similarities in structural style, orientation and degree of deformation of Miocene and Mesozoic strata suggest that Late Miocene regional folding may have accounted for a significant part of the observed deformation in older basement strata previously ascribed to earlier orogenies.A regional comparison of ages of recognized igneous and tectonic event at different latitudes in the central and southern Andes shows the gross chronology of Cenozoic events which can be correlated with sea-floor spreading and subduction events.     

XMM-Newton observations of the isolated neutron star 1RXS J214303.7+065419/RBS1774

We report XMM-Newton observations of the isolated neutron star RBS1774 and confirm its membership as an XDINS. The X-ray spectrum is best fit with an absorbed blackbody with temperature kT=101 eV and absorption edge at 0.7 keV. No power law component is required. An absorption feature in the RGS data at 0.4 keV is not evident in the EPIC data, but it is not possible to resolve this inconsistency. The star is not seen in the UV OM data to m _AB ∼21. There is a sinusoidal variation in the X-ray flux at a period of 9.437 s with an amplitude of 4%. The age as determined from cooling and magnetic field decay arguments is 10⁵–10⁶ yr for a neutron star mass of 1.35–1.5 M_⊙.      

Statistical inference in the presence of an inclination effect in laboratory radiative shock experiments

A laser-driven experiment produces images of dense shocked material by x-ray transmission. The post-shock material is sufficiently dense that no significant signal passes through the dense layer, and therefore the shock compression cannot be directly measured by comparing transmitted intensities. One could try to determine the shock compression ratio by observing the ratio of the total distance travelled by the shock to the dense post-shock layer width, but small deviations of the angle of the shock with respect to the angle of imaging create large asymmetric errors in observation. A statistical approach to recovering shock compression by appropriately combining data from several experiments is developed, using fits to a simple model for the shock and shock tube geometry.     

Statistics of magnetic fields for OB stars

Based on an analysis of the catalog of magnetic fields, we have investigated the statistical properties of the mean magnetic fields for OB stars. We show that the mean effective magnetic field B of a star can be used as a statistically significant characteristic of its magnetic field. No correlation has been found between the mean magnetic field strength B and projected rotational velocity of OB stars, which is consistent with the hypothesis about a fossil origin of the magnetic field. We have constructed the magnetic field distribution function for B stars, F(B), that has a power-law dependence on B with an exponent of ≈−1.82. We have found a sharp decrease in the function F(B) for B ⩽ 400 G that may be related to rapid dissipation of weak stellar surface magnetic fields.     

Accessory silicate mineral assemblages in the Bilanga diogenite: A petrographic study

Abstract— The petrographic relationships in diogenites between orthopyroxene and minor phases such as chromite, troilite, diopside, plagioclase, and silica are often obscured by the intense brecciation that characterizes these meteorites. Although brecciated, Bilanga preserves numerous clasts displaying primary textural relations between orthopyroxene and these minor phases that are large enough to analyze by electron microprobe. In this study, we focus on the distribution, composition, and origin of the minor phases in Bilanga to provide new insights into the crystallization and metamorphic history of these rocks. The samples examined consist mainly of orthopyroxene grains plus five types of assemblages containing diopside + a Fe‐rich phase (chromite, troilite, and/or Fe‐Ni metal) ± plagioclase ± silica. We interpret type 1 assemblages as being remnants of intercumulus melt trapped in the interstices between orthopyroxene grains after crystal settling in a magma chamber. Type 2 assemblages appear to have formed by heterogeneous exsolution during thermal metamorphism. Type 3 assemblages are believed to be remnants of other assemblages that have been shocked, melted, and rapidly recrystallized by impact events. Type 4 assemblages consist of veins that also appear to have formed from trapped intercumulus melt. Regions of silica‐rich mesostasis (type 5) appear to be larger patches of more evolved intercumulus melt that have been significantly affected by late‐stage impact melting. Finally, large clasts containing plagioclase ± diopside are interpreted to be exotic fragments of a different but possibly related rock type incorporated in the Bilanga breccia.     

3.8-μm photometry during the secondary eclipse of the extrasolar planet HD 209458b

We report infrared photometry of the extrasolar planet HD 209458b during the time of secondary eclipse (planet passing behind the star). Observations were acquired during two secondary eclipses at the NASA Infrared Telescope Facility (IRTF) in 2003 September. We used a circular variable filter (1.5 per cent bandpass) centred at 3.8 μm to isolate the predicted flux peak of the planet at this wavelength. Residual telluric absorption and instrument variations were removed by offsetting the telescope to nearby bright comparison stars at a high temporal cadence. Our results give a secondary eclipse depth of 0.0013 ± 0.0011, not yet sufficient precision to detect the eclipse, whose expected depth is  ∼0.002 –0.003  . We here elucidate the current observational limitations to this technique, and discuss the approach needed to achieve detections of hot Jupiter secondary eclipses at 3.8 μm from the ground.