Asteroid motion near the 3 : 1 resonance

A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations.     

Coupled atmosphere-ocean models of Titan's past

We have developed a coupled atmosphere and ocean model of Titan's surface. The atmospheric model is a 1-D spectrally-resolved radiative-convective model. The ocean thermodynamics are based upon solution theory. The ocean, initially composed of CH4, becomes progressively enriched in ethane over time. The partial pressures of N2 and CH4 in the atmosphere are dependent on the ocean temperature and composition. We find that the resulting system is stable against a runaway greenhouse. Accounting for the decreased solar luminosity, we find that Titan's surface temperature was about 20 K colder 4 Gyr ago. Without an ocean, but only small CH4 lakes, the temperature change is 12 K. In both cases we find that the surface of Titan may have been ice covered about 3 Gyr ago. In the lakes case condensation of N2 provides the ice, whereas in the ocean case the ocean freezes. The dominant factor influencing the evolution of Titan's surface temperature is the change in the solar constant--amplified, if an ocean is present, by the temperature dependence of the solubility of N2. Accretional heating can dramatically alter the surface temperature; a surface thermal flux of 500 erg cm-2 sec-1, representative of small levels of accretional heating, results in a approximately 20 K change in surface temperatures.     

The importance of radiative transfer in stellar pulsation models

With the advent of new astrophysical opacities it seems appropriate to discuss the need for a full radiative transfer (RT) theory instead of the usual equilibrium diffusion theory used in most nonlinear pulsation codes. Early studies on the importance of RT in the calculation of light curves for Cepheid models showed little effect over diffusion theory. The new opacities though may help to explain the bump mass discrepancy problem. For RR Lyrae models the use of RT theory causes some effects both in the color differences (U-B) as well as in the light curves. New opacities help to explain the period ratios for double mode RR Lyrae and beat Cepheids. A new area of research is in the modeling of stars with high luminosity to mass ratios that show tendencies for doubling and transitions to chaos, such as W Virginis and RV Tauri stars. For these stars it has been shown that RT is necessary in calculating their light curves and that the understanding of the shock dynamics depends on the transfer of lines in the pulsating RT dependent atmospheres (Fokin 1991).     

A photometric study of the eclipsing binary V 1073 Cygni

Photoelectric observations of the eclipsing binary V 1073 Cyg have been carried out inB andV colours at the Ege University Observatory. The light curves were analyzed with the Wilson-Devinney approach. A period study reveals that the orbital period of the system is decreasing at the rate of (3.21 ± 0.17) second per century.     

Adsorption of fluoride on goethite surfaces-implications on dental epidemiology

Fluoride ion interaction with synthetically prepared goethite has been investigated over a range of pH values (4–9) and F^– concentrations (10^–3–10^–5 M). The amount of F^– retained by goethite suspensions was found to be a function of pH, media ionic strength, F^– concentration, and goethite concentration. The lowest ionic strength (0.001 M KNO₃) gave the highest adsorption medium. Uptake was minimal at pH >7 and increased with decreasing pH. Thermodynamic properties for fluoride adsorption at 298 K and 323 K were investigated. The isosteric heat of adsorption (H _r) was calculated and the heterogeneity and homogeneity of the surface examined for goethite. In view of the importance of fluoride in dental health, the interaction of fluoride on goethite in the physical environment has important implications on dental epidemiology.     

The new Russian minorities: a statistical overview

The author "presents a succinct review of the newly constituted Russian minorities situated in the former Soviet republics. Based on census data series (1897 to 1989) and original computations, the paper covers location (highest proportion of Russians in Kazakhstan, Latvia, and Estonia), concentration (predominantly urban), occupational structure (largely in industry and science), and related data on issues such as language affinities and migration."     

Fluid inclusions in upper mantle xenoliths from Northern Patagonia,Argentina: Evidence for an upper mantle diapir

Summary Three generations of fluid inclusions can be recognized in upper mantle xenoliths from alkali basalts of the Somoncura Massif, Northern Patagonia, Argentina. The first (early, primary) one consists of dense CO₂ inclusions which were trapped in the mantle-crust boundary zone (22–36 km minimum trapping depth). Their co-genetic relationship with silicate melt inclusions enables us to constrain their minimum trapping temperature at 1200°C, indicating a high temperature event in a cooler environment. The late (pseudosecondary and secondary) generations of fluid inclusions were classified in accordance with their homogenization temperature to liquid CO₂ (L1) and vapor CO₂ (L2) phase. The minimum trapping depth for the first of the late inclusions (L1) is about 16 km. In spite of the uncertainties related to this value, L1 inclusions indicate that the upper mantle rocks, of which samples were delivered by the basalts, had some residence time in the middle crust where they experienced a metasomatic event. The fact that this event did not destroy the earlier inclusions, places severe constraints on its duration. The second late inclusions (L2) are low-pressure CO₂ inclusions with a minimum trapping depth of only 2 km, presumably a shallow magma chamber of the host basalts. The succession of fluid inclusions strongly points toward a fairly fast uprising upper mantle underneath Northern Patagonia. The petrology and mineral chemistry of the peridotitic xenoliths support this view. Extensive partial melting and loss of these melts is indicated by the preponderance of harzburgites in the upper mantle underneath Northern Patagonia, a fairly unusual feature for a continental upper mantle. That depletion event as well as several metasomatic events — including those which left traces of fluid inclusions — are possibly related to a high-speed diapiric uprise of the upper mantle in this area. The path can be traced from the garnet peridotite stability field into the middle crust, a journey which must have been unusually fast. Differences in rock, mineral, and fluid inclusion properties between geographic locations suggest a diffuse and differential type of diapirism. Future studies will hopefully help to map the full extent and the highs and lows of this diapir and elucidate questions related to its origin and future.

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Fluid-Einschlüsse in Erdmantel-Xenolithen von Nord-Patagonien: Evidenz für einen Diapir im oberen Erdmantel

Zusammenfassung Erdmantel - Xenolithe in Alkali-Basalten des Somoncure Massivs, Nord-Patagonien, Argentinien, führen drei Generationen von Fluid-Einschlüssen. Die erste (frühe, primäre) Generation besteht aus dichten CO₂-Einschlüssen, welche offenbar in der Mantel-Kruste Grenzzone (22–36 km Minimum-Tiefe) eingeschlossen wurden. CO₂-Einschlüsse sind kogenetisch mit Silikat-Schmelzeinschlüssen. Dies erlaubt die Abschätzung der Einschließ-Temperatur mit minimal 1200°C, was auf ein Hochtemperatur-Ereignis in einer deutlich kühleren Umgebung hinweist. Die späten (pseudosekundäre und sekundäre) CO₂- Fluid-Einschlüsse bilden zwei Generationen von denen die eine in die flüssige (L1), die andere in die Dampfphase (L2) homogenisieren. Die minimale Einschließ-Tiefe für die L1 Generation ist etwa 16 km. Dies bedeutet - auch bei Berücksichtigung der mit diesem Wert verbundenen Ungenauigkeit - daß diese Erdmantel-Gesteine einige Zeit in der mittleren Erdkruste verbrachten und ein metasomatisches Ereignis erlebten, bevor sie von den Basalten zur Erdoberfläche gebracht wurden. Die Tatsache, daß dieses Ereignis die frühen Einschlüsse nicht zerstörte, kann nur bedeuten, daß es von kurzer Dauer war. Die L2-Generation besteht aus Niedrigdruck CO₂-Einschlüssen mit einer Minimum-Einschließtiefe von nur 2 km. Dies könnte in einer seichten Magmakammer des Wirt Basaltes geschehen sein.Die Abfolge von Fluid-Einschlüssen deutet auf einen relativ schnell aufsteigenden oberen Erdmantel unterhalb von Patagonien hin. Die Petrologie und Mineralchemie der peridotitischen Xenolithe unterstützen das. Die Vorherrschaft von Harzburgiten im Erdmantel unterhalb von Nord-Patagonien deutet auf umfangreiche Bildung partieller Schmelzen und deren Abfuhr hin — eine für einen kontinentalen Mantel ungewöhnliche Situation. Sowohl die Verarmungsereignisse, als auch die metasomatischen Veränderungen (einschließlich jene, welche Spuren in Form von Fluid Einschlüssen hinterließen) machen das Vorhandensein eines schnell aufsteigenden Daipirs im oberen Erdmantel dieser Gegend wahrscheinlich. Der Aufstieg kann vom Stabilitätsbereich der Granat-Peridotite bis in die mittlere Kruste verfolgt werden und muß daher relativ schnell erfolgt sein. Unterschiede in Gesteins-, Mineral und Fluid-Eigenschaften zwischen verschiedenen Lokalitäten legen einen diffusen und differenziellen Diapirismus nahe. Zukünftige Studien sollten es ermöglichen, das Gesamtausmaß und die unterschiedlichen Aufstiegshöhen des Diapirs zu kartieren und Hinweise auf seine Entstehung und zukünftige Entwicklung zu erhalten.

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With 5 Figures