Tidal evolution in close binary systems,II

The aim of the present investigation will be to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axisA, eccentricitye, and longitude of the periastron ), arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between 0e<1; and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.In Section 2 following brief introductory remarks the variational equations of the problem of plane motion will be set up in terms of the rectangular componentsR, S, W of disturbing accelerations with respect to a revolving system of coordinates. The explicit form of these coefficients will be established in Section 3 to the degree of accuracy to which squares and higher powers of quantities of the order of superficial distortion can be ignored. Section 4 will be devoted to a derivation of the explicit form of the variational equations for the case of a perturbing function arising from axial rotation; and in Section 5 we shall derive variational equations which govern the perturbation of orbital elements caused by lagging dynamical tides.Numerical integrations of these equations, which govern the tidal evolution of close binary systems prompted by viscous friction at constant mass, are being postponed for subsequent investigations.Prepared at the Lunar Science Institute, Houston, Texas, under the joint support of the Universities Space Research Association, Charlottesville, Virginia, and the National Aeronautics and Space Administration Manned Spacecraft Center, Houston, Texas, under Contract No. NSR 09-051-001. This paper constitutes Lunar Science Institute Contribution no. 100.Normally at the Department of Astronomy, University of Manchester, England.     

Cooling of a coronal flare loop through radiation and conduction

A simple method is proposed for a computation of the cooling of coronal flare loops by radiation and conduction, for various temperatures, densities, and lengths of the loops. The relative importance of conductive and radiative losses is briefly discussed.     

The precession and nutation of deformable bodies

The aim of the present paper will be to derive from the fundamental equations of hydrodynamics the explicit form of the Eulerian equations which govern the motion about the centre of gravity of self-gravitating bodies, consisting of compressible fluid of arbitrary viscosity, in an arbitrary external field of force. If the problem is particularized so that the external field of force represents the attaction of the sun and the moon, this motion would represent the luni-solar precession and nutation of a fluid viscous earth; if, on the other hand, the external field of force were governed by the earth (and the sun), the motion would define the physical librations of the moon regarded as a deformable body. The same equations are, moreover, equally applicable to the phenomena of precession and nutation of rotating fluid components in close binary systems, distorted by mutual tidal action; and the present paper contains the first formulation of the effects of viscosity on such phenomena.Investigation supported in part by the U.S. National Aeronautics and Space Administration under Contract No. NASW-1470.     

Origin of the Okrouhlá Radouň episyenite-hosted uranium deposit,Bohemian Massif,Czech Republic: fluid inclusion and stable isotope constraints

The Okrouhlá Radouň shear zone hosted uranium deposit is developed along the contact of Variscan granites and high-grade metasedimentary rocks of the Moldanubian Zone of the Bohemian Massif. The pre-ore pervasive alteration of wall rocks is characterized by chloritization of mafic minerals, followed by albitization of feldspars and dissolution of quartz giving rise to episyenites. The subsequent fluid circulation led to precipitation of disseminated uraninite and coffinite, and later on, post-ore quartz and carbonate mineralization containing base metal sulfides. The fluid inclusion and stable isotope data suggest low homogenization temperatures (～50–140 °C during pre-ore albitization and post-ore carbonatization, up to 230 °C during pre-ore chloritization), variable fluid salinities (0–25 wt.% NaCl eq.), low fluid δ¹⁸O values (?10 to +2 ‰ V-SMOW), low fluid δ¹³C values (?9 to ?15 ‰ V-PDB), and highly variable ionic composition of the aqueous fluids (especially Na/Ca, Br/Cl, I/Cl, SO₄/Cl, NO₃/Cl ratios). The available data suggest participation of three fluid endmembers of primarily surficial origin during alteration and mineralization at the deposit: (1) local meteoric water, (2) Na–Ca–Cl basinal brines or shield brines, (3) SO₄–NO₃–Cl–(H)CO₃ playa-like fluids. Pre-ore albitization was caused by circulation of alkaline, oxidized, and Na-rich playa fluids, whereas basinal/shield brines and meteoric water were more important during the post-ore stage of alteration.     

Mineralogical and geochemical evidence for multi-stage origin of mineral veins hosted by teschenites at Tichá, Outer Western Carpathians,Czech Republic

Numerous mineral veins are hosted in a body of teschenite which is situated within the Lower Cretaceous flysch siliciclastics of the Silesian Unit at Tichá. Mineralogy, fluid inclusions, stable isotopes and trace elements have been studied in order to assess the origin of this mineralization. Three stages of vein cementation have been recognized, each of them being characterized by distinct mineral composition and genetic conditions. The first stage is composed of titanite, aegirine-augite to aegirine, annite, analcime and strontian apatite. These minerals originated from NaCl-rich, CaCl₂-poor magmatic brine (total fluid salinities range between 47 and 57 wt%), leaving after crystallization of host teschenite in low-pressure (<1 kbar) environment. Crystallization temperatures reached ～390–510 °C for early phases, titanite and aegirine-augite. The second stage is formed by calcite, chlorite, dolomite, siderite, strontianite, quartz, pyrite and sphalerite. The parent fluids were low-salinity (0.5–4.5 wt% NaCl eq.) aqueous solutions with low content of strong REE-complexing ligands, that were progressively cooled during mineral precipitation (up to ～190 °C at the beginning, ～90 °C at the end of crystallization). These fluids are interpreted to be predominantly of external origin, derived from surrounding sedimentary sequences during diagenetic dewatering of clay minerals. The highly positive δ¹⁸O and near-zero δ¹³C values indicate an interaction of fluids with sedimentary carbonates. The third stage is formed by a dense net of calcite veinlets, which probably originated during tectonic deformations connected with orogenetic movements during the Tertiary. The source of strontium for first stage mineralization was probably related to the special conditions of magmatic evolution of the host teschenite, whereas strontium for second stage minerals could have been remobilized during hydrothermal alteration from earlier teschenite-hosted mineral phases and/or limestone.     

Geochemical characteristics of the high- and low-Ti basaltic rocks from the uplifted shoulder of the Ohře (Eger) Rift,Western Bohemia

High-Ti melanephelinite (3.8–5.9 wt% TiO₂), medium-Ti (phono)tephrite (2.7–3.1 wt% TiO₂), and low-Ti olivine melanephelinite/basanite (1.9–2.3 wt.% TiO₂) are subordinate rock types in the central European Cenozoic Volcanic Province. A contrasting melanephelinite to (phono)tephrite series occurs in the Lou?ná–Oberwiesenthal Volcanic Centre (37–28 Ma) and also as satellite volcanic bodies (26–12 Ma) together with olivine melanephelinite/basanite (17–20 Ma) on the southwestern periphery of the Kru?né hory mountains (Erzgebirge). The volcanic rocks intrude the Variscan basement of the uplifted shoulder of the Oh?e/Eger Rift in the Kru?né hory mountains of the Bohemian Massif. Low Mg# (44–59) and Cr, Ni contents and enrichment of LILE, Zr, Hf, Nb, Ta, U, Th and LREE in the high-Ti melanephelinites contrast with the composition of primitive low-Ti olivine melanephelinites/basanites displaying high Mg# (63–74) and high contents of compatible elements. The high-Ti melanephelinites reveal a wide range in initial ⁸⁷Sr/⁸⁶Sr of ca. 0.7034–0.7038 and ε_Nd of 2.4–4.9. The low-Ti melanephelinites show an overlapping range of initial ⁸⁷Sr/⁸⁶Sr of ca. 0.7035–0.7036 and ε_Nd of 4.3–5.5. The large variation in initial ⁸⁷Sr/⁸⁶Sr ratios at similar ε_Nd values in those rock types is interpreted as evidence for melting of metasomatized lithospheric mantle sources comprising K-bearing phases with radiogenic Sr. Modification of the olivine-free alkali basaltic magmas by differentiation or crustal contamination could give rise to the medium-Ti (phono) tephrites. The initial isotope ratios of all samples are consistent with HIMU-mantle sources and contributions from lithospheric mantle. The olivine-free melanephelinitic rocks often contain alkali pyroxenite–ijolite xenoliths with initial ⁸⁷Sr/⁸⁶Sr ratios of ca. 0.7036 and ε_Nd of 3.0. We interpret these xenoliths as samples of an intra-crustal alkali complex derived from similar mantle sources as those for the basaltic volcanic rocks.     

Sensitivity of Ceres-Maize Yields to Statistical Structure of Daily Weather Series

To study impacts of climate variations on cropproduction, the growth models are used to simulateyields in present vs. changed climate conditions.Met&Roll is a four-variate (precipitation amount,solar radiation, minimum and maximum temperatures) stochasticweather generator used to supply synthetic dailyweather series for the crop growth model CERES-Maize.Three groups of experiments were conducted in thisstudy: (1) Validation of Met&Roll reveals some discrepanciesin the statistical structure of synthetic weatherseries, e.g., (i) the frequency of occurrence of longdry spells, extreme values of daily precipitationamount and variability of monthly means areunderestimated by the generator; (ii) correlations andlag-1 correlations among weather characteristicsexhibit a significant annual cycle not assumed by themodel. On the whole, the best fit of the observed andsynthetic weather series is experienced in summermonths. (2) The Wilcoxon test was employed to comparedistributions of maize yields simulated with use ofobserved vs. synthetic weather series. As nostatistically significant differences were detected,it is assumed that the generator imperfections inreproducing the statistical structure of weatherseries negligibly affect the model yields. (3) Thesensitivity of model yields to selectedcharacteristics of the daily weather series wasexamined. Emphasis was placed on the characteristicsnot addressed by typical GCM-based climate changescenarios: daily amplitude of temperature, persistenceof the weather series, shape of the distribution ofdaily precipitation amount, and frequency ofoccurrence of wet days. The results indicate that someof these characteristics may significantly affect cropyields and should therefore be considered in thedevelopment of climate change scenarios.