On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

Is the transition impact to post‐impact rock complete? Some remarks based on XRF scanning,electron microprobe,and thin section analyses of the Yaxcopoil‐1 core in the Chicxulub crater

Abstract The transition from impact to post‐impact rocks in the Yaxcopoil‐1 (Yax‐1) core is marked by a 2 cm‐thick clay layer characterized by dissolution features. The clay overlies a 9 cm‐thick hardground, overlying a 66 cm‐thick crossbedded unit, consisting of dolomite sandstone alternating with thin micro‐conglomerate layers with litho‐ and bioclasts and the altered remains of impact glass, now smectite. The micro‐conglomerates mark erosion surfaces. Microprobe and backscatter SEM analysis of the dolomite rhombs show an early diagenetic, complex‐zoned, idiomorphic overgrowth, with Mn‐rich zones, possibly formed by hot fluids related to cooling melt sheet in the crater. The pore spaces are filled with several generations of coelestite, barite, K‐feldpar, and sparry calcite. XRF core scanning analysis detected high Mn values in the crossbedded sediments but no anomalous enrichment of the siderophile elements Cr, Co, Fe, and Ni in the clay layer. Shocked quartz occurs in the crossbedded unit but is absent in the clay layer. The basal Paleocene marls are strongly dissolved and do not contain a basal Paleocene fauna. The presence of a hardground, the lack of siderophile elements, shocked quartz, or Ni‐rich spinels in the clay layer, and the absence of basal Paleocene biozones P0 and Pa all suggest that the top of the ejecta sequence and a significant part of the lower Paleocene is missing. Due to the high energy sedimentation infill, a hiatus at the top of the impactite is not unexpected, but there is nothing in the biostratigraphy, geochemistry, and petrology of the Yax‐1 core that can be used to argue against the synchroneity of the end‐Cretaceous mass‐extinctions and the Chicxulub crater.     

Geochemistry of metabauxites in the Bergsträsser Odenwald (Mid German Crystalline Rise) and palaeoenvironmental implications

Summary Pre- to early Variscan metamorphosed volcano-sedimentary series of the western (Bergstr?sser) Odenwald have been intruded by Variscan calc-alkaline magmatites with plate margin affinities. Within the NE-SW trending metabasic and metapelitic series, intercalations of anomalously aluminous- and iron-rich compositions representing former bauxites are distinguishable. Geochemical data indicate that the Al-, Fe-rich rocks are the metamorphic equivalents of a former bauxitic-ferralitic weathering profile, now comprising spinel fels (top) with relics of pisolitic structures, corundum-chlorite fels, corundum-cordierite-plagioclase gneiss, sillimanite-cordierite-plagioclase gneiss, cordierite-plagioclase gneiss and kinzigite (base) displaying a decrease of weathering in the order as listed. The evolution of such terrestrial sediments is related to specific climatic, environmental, and physico-chemical conditions similar to those of the present-day tropical to subtropical humid regions with high seasonal rains and intensive drainage. Comparison with palaeomagnetic and palaeoclimatic data indicate that the Odenwald metabauxites originally formed during the Lower to Mid-Devonian. Our results imply that, during this geological time span, parts of the precursors of the Mid-German Crystalline Rise not only transversed low latitudes but also were exposed to terrestrial weathering.

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Zusammenfassung Die Geochemie der Metabauxite im Bergstr?sser Odenwald (Mitteldeutsche Kristallinschwelle) und ihre Bedeutung für das Pal?omilieu Im westlichen (Bergstr?sser) Odenwald intrudierten variszische Plattenrand-Kalkalkali-Magmatite in pr?- bis früh-variszische, ehemalige vulkano-sediment?re Serien. Innerhalb der heute NE-SW streichenden Metabasit- und Metapelitzüge treten lokal Al-Fe-reiche Einschaltungen auf, die strukturell und geochemisch als metamorphe ?quivalente eines ehemaligen bauxitisch-ferralitischen Verwitterungsprofils klassifiziert werden k?nnen. Sie umfassen Spinellfelse mit erhaltenen, ehemaligen zonierten Pisolithen, Korund-Chloritfelse, Korund-Cordierit-Plagioklasgneise, Sillimanit-Cordierit-Plagioklasgneise, Cordierit-Plagioklasgneise und Kinzigite. Bauxite k?nnen als terrestrische Bildungen nur unter speziellen klimatischen und physiko-chemischen Bedingungen entstehen. Pal?omagnetische und pal?oklimatische Daten legen die Bildung der ehemaligen Bauxite im unteren bis mittleren Devon nahe. Daraus folgt, da? w?hrend dieser geologischen Zeitspanne die Vorl?ufer der mitteldeutschen Kristallinschwelle bei der Norddrift nicht nur ?quatorn?he passierten, sondern auch partiell ungest?rte, terrestrische, tropisch-subtropische Verwitterungsprozesse abliefen.

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Received June 10, 1999; revised version accepted October 30, 2000     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

Can the big-bang singularity be avoided in the scale-covariant theory?

The Raychaudhuri equation is written in terms of atomic units in the scale-covariant theory of Canutoet al. (1977) and it is pointed out that even dust-filled nonrotating cosmological models may not have an observable singularity of infinite density in the beginning. Simple explicit solutions of Einstein's equations are also constructed in terms of atomic units and its is shown that the Einstein-de Sitter solution in gravitational units may appear to be a static or an oscillating universe in atomic units.     

The dust coma of periodic comet Churyumov-Gerasimenko (1982 VIII)

The dust coma of Comet P/Churyumov-Gerasimenko was monitored in the infrared (1–20 μm) from September 1982 to March 1983. Maximum dust production rate of ～2 × 10⁵ g/sec occured in December, 1 month postperihelion. The ratio of dust/gas production was higher than that in other short-period comets. No silicate feature was visible in the 8- to 13-μm spectrum on 23 October. The mean geometric albedo of the grains was ～0.04 at 1.25 μm and ～0.05 at 2.2 μm.     

Zircon U–Pb age, trace element and Hf isotope composition of Kongling terrane in the Yangtze Craton: refining the timing of Palaeoproterozoic high-grade metamorphism

U–Pb age, trace element and Hf isotope compositions of zircon were analysed for a metasedimentary rock and two amphibolites from the Kongling terrane in the northern part of the Yangtze Craton. The zircon shows distinct morphological and chemical characteristics. Most zircon in an amphibolite shows oscillatory zoning, high Th/U and ¹⁷⁶Lu/¹⁷⁷Hf ratios, high formation temperature, high trace element contents, clear negative Eu anomaly, as well as HREE-enriched patterns, suggesting that it is igneous. The zircon yields a weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 2857 ± 8 Ma, representing the age of the magmatic protolith. The zircon in the other two samples is metamorphic. It has low Th/U ratios, low trace element concentrations, variable HREE contents (33.8 ≥ Lu_N≥2213; 14.7 ≤ Lu_N/Sm_N ≤ 354) and ¹⁷⁶Lu/¹⁷⁷Hf ratios (0.000030–0.001168). The data indicate that the zircon formed in the presence of garnet and under upper amphibolite facies conditions. The metamorphic zircon yields a weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 2010 ± 13 Ma. These results combined with previously obtained Palaeoproterozoic metamorphic ages suggest a c. 2.0 Ga Palaeoproterozoic collisional event in the Yangtze Craton, which may result from the assembly of the supercontinent Columbia. The zircon in two samples yields weighted mean two-stage Hf model ( T _DM2) ages of 3217 ± 110 and 2943 ± 50 Ma, respectively, indicating that their protoliths were mainly derived from Archean crust.     

Age and early metamorphic history of the Sanbagawa belt: Lu–Hf and P–T constraints from the Western Iratsu eclogite

Two distinct age estimates for eclogite-facies metamorphism in the Sanbagawa belt have been proposed: (i) c.  120–110 Ma based on a zircon SHRIMP age for the Western Iratsu unit and (ii) c.  88–89 Ma based on a garnet–omphacite Lu–Hf isochron age from the Seba and Kotsu eclogite units. Despite the contrasting estimates of formation ages, petrological studies suggest the formation conditions of the Western Iratsu unit are indistinguishable from those of the other two units—all ∼20 kbar and 600–650 °C. Studies of the associated geological structures suggest the Seba and Western Iratsu units are parts of a larger semi-continuous eclogite unit. A combination of geochronological and petrological studies for the Western Iratsu eclogite offers a resolution to this discrepancy in age estimates. New Lu–Hf dating for the Western Iratsu eclogite yields an age of 115.9 ± 0.5 Ma that is compatible with the zircon SHRIMP age. However, petrological studies show that there was significant garnet growth in the Western Iratsu eclogite before eclogite facies metamorphism, and the early core growth is associated with a strong concentration of Lu. Pre-eclogite facies garnet (Grt1) includes epidote–amphibolite facies parageneses equilibrated at 550–650 °C and ∼10 kbar, and this is overgrown by prograde eclogite facies garnet (Grt2). The Lu–Hf age of c.  116 Ma is strongly skewed to the isotopic composition of Grt1 and is interpreted to reflect the age of the pre-eclogite phase. The considerable time gap ( c.  27 Myr) between the two Lu–Hf ages suggests they may be related to separate tectonic events or distinct phases in the evolution of the Sanbagawa subduction zone.