A moment method for radiative transfer in an anisotropically-scattering slab medium with space-dependent albedoω(x)

The moment method is used to solve the radiative transfer problem in an anisotropic scattering plane medium with arbitrary space-dependent albedo(x). The results are compared with those obtained recently by Cengel and Özisik.     

On ‘bimodality of the solar cycle’ and the duration of cycle 21

The period-growth dichotomy of the solar cycle predicts that cycle 21, the present solar cycle, will be of long duration (>133 mo), ending after July 1987. Bimodality of the solar cycle (i.e., cycles being distributed into two groups according to cycle length, based on a comparison to the mean cycle period) is clearly seen in a scatter diagram of descent versus ascent durations. Based on the well-observed cycles 8–20, a linear fit for long-period cycles (being a relatively strong inverse relationship that is significant at the 5% level and having a coefficient of determination r ² 0.66) suggests that cycle 21, having an ascent of 42 mo, will have a descent near 99 mo; thus, cycle duration of about 141 mo is expected. Like cycle 11, cycle 21 occurs on the downward envelope of the sunspot number curve, yet is associated with an upward first difference in amplitude. A comparison of individual cycle, smoothed sunspot number curves for cycles 21 and 11 reveals striking similarity, which suggests that if, indeed, cycle 21 is a long-period cycle, then it too may have an extended tail of sustained, low, smoothed sunspot number, with cycle 22 minimum occurring either in late 1987 or early 1988.     

On the proposed associations of solar neutrino flux with solar particles,cosmic rays,and the solar activity cycle

It has been proposed that the observed solar neutrino flux exhibits important correlations with solar particles, galactic cosmic rays, and the sunspot cycle, with the latter correlation being opposite in phase and lagging behind the sunspot cycle by about one year. Re-examination of the data-available interval 1971–1981, employing various tests of statistical significance, however, suggests that such a claim is, at present, unwarrantable. For example, on the associations of solar neutrino flux and cosmic-ray flux with the Ap geomagnetic index, neither were found to be statistically significant (at the 95% level of confidence), regardless of the choice of lag (-1, 0, or +1 yr). Presuming linear fits, all correlations with Ap had coefficients of determination (r ², where r is the linear correlation coefficient) less than 16%, meaning that 16% of the variation in the selected test parameters could be explained by the variation in Ap. Similarly, on the associations of solar neutrino flux and cosmic ray flux with sunspot number, only the latter association proved to be of statistical importance. Using the best linear fits, the correlation between yearly averages of solar neutrino flux and sunspot number had r ² 19%, the correlation between weighted moving averages (of order 5) of solar neutrino flux and sunspot number had r ² 45%, and the correlation between cosmic-ray flux and sunspot number had r ² 76%, all correlations being inverse associations. Solar neutrino flux was found not to correlate strongly with cosmic-ray flux, and the Ap geomagnetic index was found not to correlate strongly with sunspot number.     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

Accuracy of close binary mass determinations from parallaxes

Absolute masses for W Ursae Majoris and Algol-type close binaries can be determined from their parallax, if observed, and the relative sizes of the stars and their mass ratio, obtained from a light curve solution. An error propagation study compares the typical order of magnitude of the various terms involved, and shows how accurate parallaxes have to be in order to make the procedure work, i.e., making the parallax term not larger than the combined non-parallax terms, and producing reasonably low mass errors. Some comments are made on the possibilities with respect to the HIPPARCOS program.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).     

U–Pb SHRIMP zircon geochronology and T–t–d history of the Kampa Dome, southern Tibet

Structural, petrographic and geochronologic studies of the Kampa Dome provide insights into the tectonothermal evolution of orogenic crust exposed in the North Himalayan gneiss domes of southern Tibet. U–Pb ion microprobe dating of zircons from granite gneiss exposed at the deepest levels within the dome yields concordia ²⁰⁶Pb/²³⁸U age populations of 506 ± 3 Ma and 527 ± 6 Ma, with no evidence of new zircon growth during Himalayan orogenesis. However, the granite contains penetrative deformation fabrics that are also preserved in the overlying Paleozoic strata, implying that the Kampa granite is a Cambrian pluton that was strongly deformed and metamorphosed during Himalayan orogenesis. Zircons from deformed leucogranite sills that cross-cut Paleozoic metasedimentary rocks yield concordant Cambrian ages from oscillatory zoned cores and discordant ages ranging from ca. 491–32 Ma in metamict grains. Since these leucogranites clearly post-date the metasedimentary rocks they intrude, the zircons are interpreted as xenocrysts that are probably derived from the Kampa granite. The Kampa Dome formed via a series of progressive orogenic events including regional ~ N–S contraction and related crustal thickening (D₁), predominately top-to-N ductile shearing and crustal extension (D₂), top-to-N brittle–ductile faulting and related folding on the north limb of the dome, localized top-to-S faulting on the southern limb of the dome, and crustal doming (D₃), and continued N–S contraction, E–W extension and doming (D₄). Structural and geochronologic variability amongst adjacent North Himalayan gneiss domes may reflect changes in the magnitude of crustal exhumation along the North Himalayan antiform, possibly relating to differences in the mid-crustal geometry of the exhuming fault systems.     

Upwelling, species, and depth effects on coral skeletal cadmium-to-calcium ratios (Cd/Ca)

Skeletal cadmium-to-calcium (Cd/Ca) ratios in hermatypic stony corals have been used to reconstruct changes in upwelling over time, yet there has not been a systematic evaluation of this tracer’s natural variability within and among coral species, between depths and across environmental conditions. Here, coral skeletal Cd/Ca ratios were measured in multiple colonies of Pavona clavus, Pavona gigantea and Porites lobata reared at two depths (1 and 7 m) during both upwelling and nonupwelling intervals in the Gulf of Panama (Pacific). Overall, skeletal Cd/Ca ratios were significantly higher during upwelling than during nonupwelling, in shallow than in deep corals, and in both species of Pavona than in P. lobata. P. lobata skeletal Cd/Ca ratios were uniformly low compared to those in the other species, with no significant differences between upwelling and nonupwelling values. Among colonies of the same species, skeletal Cd/Ca ratios were always higher in all shallow P. gigantea colonies during upwelling compared to nonupwelling, though the magnitude of the increase varied among colonies. For P. lobata, P. clavus and deep P. gigantea, changes in skeletal Cd/Ca ratios were not consistent among all colonies, with some colonies having lower ratios during upwelling than during nonupwelling. No statistically significant relationships were found between skeletal Cd/Ca ratios and maximum linear skeletal extension, δ¹³C or δ¹⁸O, suggesting that at seasonal resolution the Cd/Ca signal was decoupled from growth rate, coral metabolism, and ocean temperature and salinity, respectively. These results led to the following conclusions, (1) coral skeletal Cd/Ca ratios are independent of skeletal extension, coral metabolism and ambient temperature/salinity, (2) shallow P. gigantea is the most reliable species for paleoupwelling reconstruction and (3) the average Cd/Ca record of several colonies, rather than of a single coral, is needed to reliably reconstruct paleoupwelling events.     

Thermal evolution and physics of melt extraction on the ureilite parent body

We develop a physical model of the thermal history of the ureilite parent body (UPB) that numerically tracks the history of its heating, hydration, dehydration, partial melting and smelting as a function of its formation time and the initial values of its composition, formation temperature and water ice content. Petrologic and chemical data from the main group (non-polymict) ureilite meteorites, which sample the interior of the UPB between depths corresponding to pressures in the range 3-10 MPa, are used to constrain the model. We find that to achieve the ∼30% melting inferred for ureilites from all sampled depths, the UPB must have had a radius between ∼80 and ∼130 km and must have accreted about 0.55 Ma after CAI formation. Melting began in the body at ∼1 Ma after CAI, and the time at which 30% melting was reached varied with depth in the asteroid but was always between ∼4.5 and ∼5.8 Ma after CAI. The total rate at which melt was produced in the UPB varied from more than 100 m³ s⁻¹ in the very early stages of melting at ∼1 Ma after CAI to ∼5 m³ s⁻¹ between 2 and 3 Ma after CAI, decreasing to extremely small values as the end of melting was approached beyond ∼5 Ma. Although the initial period of high melt production occupied only a short time around 1 Ma after CAI, it corresponded to ∼half (16%) of total silicate melting, and all strictly basaltic (i.e. plagioclase-saturated) melts must have been produced during this period.A very efficient melt transport network, consisting of a hierarchy of veins and larger pathways (dikes), developed quickly at the start of melting, ensuring rapid (timescales of months) transport of any single parcel of melt to shallow levels, thus ensuring that chemical interaction between melts and the rocks through which they subsequently passed was negligible. Volatile (mainly carbon monoxide) production due to smelting began at the start of silicate melting in the shallowest parts of the UPB and at later times at greater depths. Except at the very start and very end of melting, the volatile content of the melts produced was always high - generally between 15 and 35 mass % - and most of the melt produced was erupted at the surface of the UPB with speeds well in excess of the escape velocity and was lost into space. However, we show that 30% melting at the 3 MPa pressure level was only possible if ∼15% of the total melt produced in the asteroid was retained as a small number (∼5) of very extensive, sill-like intrusions centered at a depth of ∼7 km below the surface, near the base of the ∼8 km thick outer crust of the asteroid that was maintained at temperatures below the basalt solidus by conductive heat loss to the surface. The horizontal extents of these sills occupied about 75% of the surface area of the UPB, and the sills acted as buffers between the steady supply of melt from depth and the intermittent explosive eruption of the melt into space. We infer that samples from these intrusions are preserved as the rare feldspathic (loosely basaltic) clasts in polymict ureilites, and show that the cooling histories of the sills are consistent with these clasts reaching isotopic closure at ∼5 Ma after CAI, as given by ²⁶Al-²⁶Mg, ⁵³Mn-⁵³Cr and Pb-Pb age dates.     

Density functional theory predictions of equilibrium isotope fractionation of iron due to redox changes and organic complexation

We present molecular orbital/density functional theory (MO/DFT) calculations that predict a greater isotopic fractionation in redox reactions than in reactions involving ligand exchange. The predicted fractionation factors, reported as 1000·ln(^56-54α), associated with equilibrium between Fe-organic and Fe-H₂O species were <1.6‰ in vacuo and <1.2‰ in solution when the oxidation state of the system was held constant. These fractionation factors were significantly smaller than those predicted for equilibrium between different oxidation states of Fe, for which 1000·ln(^56-54α) was >2.7‰ in vacuo and >2.2‰ in solution when the bound ligands were unchanged. The predicted ⁵⁶Fe/⁵⁴Fe ratio was greater in complexes containing Fe³⁺ and in complexes with shorter Fe-O bond lengths; both of these trends follow previous theoretical results. Our predictions also agree with previous experimental measurements that suggest that the largest biological fractionations will be associated with processes that change the oxidation state of Fe, and that identification of biologically controlled Fe isotope fractionation may be difficult when abiotic redox fractionations are present in the system. The models studied here also have important implications for future theoretical isotope calculations, because we have discovered the necessity of using vibrational frequencies instead of reduced masses when predicting reduced partition functions in aqueous-phase species.     

Uranophane dissolution and growth in CaCl2-SiO2(aq) test solutions

The dissolution and growth of uranophane [Ca(UO₂)₂(SiO₃OH)₂·5H₂O] have been examined in Ca- and Si-rich test solutions at low temperatures (20.5 ± 2.0 °C) and near-neutral pH (∼6.0). Uranium-bearing experimental solutions undersaturated and supersaturated with uranophane were prepared in matrices of ∼10⁻² M CaCl₂ and ∼10⁻³ M SiO₂(aq). The experimental solutions were reacted with synthetic uranophane and analyzed periodically over 10 weeks. Interpretation of the aqueous solution data permitted extraction of a solubility constant for the uranophane dissolution reaction and standard state Gibbs free energy of formation for uranophane ( kJ mol⁻¹).