On the Distance Function Between Two Keplerian Elliptic Orbits

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the collapse of a vertical packet of mixed patches. Laboratory and field studies

Visualization of a collapsing vertical packet of patches in a laboratory experiment and the results of acoustical sounding under field conditions allowed us to discriminate the stage of its evolution which was previously unknown. It is defined by the variations of the horizontal dimensions of patches and their effective scattering surface with a period ofT=150–250/N, whereN is the Brunt-Väisälä frequency. The horizontal dimensions of patches can reach 40% of their final dimensions at the evolution stage discriminated.Translated by Mikhail M. Trufanov.     

Tellurides from Sunrise Dam gold deposit, Yilgarn Craton, Western Australia: a new occurrence of nagyágite

Summary The Cu–Fe–Au–Mo (W) deposits in southeastern Hubei are an important component of the Middle–Lower Yangtze River metallogenic belt. Molybdenite from the Fengshandong Cu- (Mo), Ruanjiawan W–Cu- (Mo), Qianjiawan Cu–Au, Tongshankou Cu–Mo and Tonglüshan Cu- (Fe) deposits yielded Re–Os ages of 144.0 ± 2.1 Ma, 143.6 ± 1.7 Ma, 137.7 ± 1.7 Ma, 142.3 ± 1.8–143.7 ± 1.8 Ma and 137.8 ± 1.7–138.1 ± 1.8 Ma, respectively. Phlogopite from the Tieshan Fe- (Cu) deposit yielded an Ar–Ar age of 140.9 ± 1.2 Ma. These data and other published isotopic ages (Re–Os molybdenite and Ar–Ar mica ages) for the Cu–Fe–Au–Mo (W) deposits in the Middle–Lower Yangtze River metallogenic belt show that Cu–Fe–Au–Mo (W) mineralisation in the Tongling, Anqing, Jiurui and Edong ore districts developed in a narrow time span between 135.5 and 144.9 Ma, reflecting an important regional metallogenic event. An integrated study of available petrological and geochronological data, together with relationships to magmatism and the regional geodynamic framework, indicate that the Cu–Fe–Au–Mo (W) mineralisation in the Middle–Lower Yangtze River belt occurred during a regime of lithospheric extension. This extension is probably related to Late Mesozoic processes of lower crustal delamination and lithospheric thinning in East China.     

Stability and phase relations of nonstoichiometric clinopyroxenes in the join diopside-Ca-Eskola component at high pressures

The stability of nonstoichiometric clinopyroxenes in the Di-CaEsk join was experimentally studied, and phase diagrams were constructed for this join at pressures of 2.0 and 3.0 GPa. It was found that melting in the diopside part of the join occurs at anomalously low temperatures, and nonstoichiometric clinopyroxene coexists with a phase approaching diopside in composition. Phase relations along the Di-CaEsk join can be described and consistently interpreted only assuming that the diopside phase (α-diopside) is thermodynamically stable. The following phase volumes were observed along the solidus of the join at a pressure of 3.0 GPa: Cpx, αDi+Cpx, αDi+Cpx+Qtz, αDi+Cpx+Grt+Qtz, Cpx+Grt+Qtz, Cpx+Grt+Ky+Qtz, Grt+Ky+Qtz. Melting occurs via the eutectic reaction αDi+Cpx+Grt+Qtz=L at a temperature of about 1200°C in the diopside part of the system and via the eutectic reaction Cpx+Grt+Ky+Qtz=L at a temperature of 1400°C in the calcium-rich part of the system. At a pressure of 2.0 GPa, melting occurs at temperatures of 1200–1300°C via the eutectic reaction αDi+Cpx+ An + Qtz=L. The invariant equilibrium (L, An, Cpx, Grt, αDi, Qtz) lies within the pressure range 2.0–3.0 GPa. Nonstoichiometric clinopyroxenes form complex solid solutions, the compositions of which are not strictly confined to the Di-CaEsk join and depend on temperature, pressure, and phase association. Grossular garnets coexist with nonstoichiometric clinopyroxenes and α-diopside.     

Modeling of deep-seated high-alumina parageneses on the basis of the stability fields of corundum- and spinel-normative assemblages of the system CaO–MgO–Al2O3–SiO2

To elaborate physicochemical models for the origin of crystalline rocks, experimental studies of the field of high-alumina assemblages of the system CaO–MgO–Al₂O₃–SiO₂ were carried out at 10–30 kbar and 1250–1535 °C. We have determined the phase relations between the melt (L) and An, Sp, Cpx, Cor, and Ga, the slope of the rays of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx +Ga + Cor + Sp, the position of the nonvariant point (An, Sp, Cpx, Cor, Ga, L), and the compositions of phases participating in these reactions. Based on a topological analysis of the studied segment of the system CaO–MgO–Al₂O₃–SiO₂, we have substantiated that “eclogitization” must follow the reaction Opx + An + Sp = Cpx + Ga. A fundamental continuous series of eutectic monovariant equilibria was observed: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx (+ Ga) + An + Sp, and L = Cpx + Cor (+ Ga) + An. A change in the melt composition in this series of eutectic reactions depending on pressure must reflect the most likely magma genesis trend in nature. Comparision of the composition fields in which the above series of reactions is observed with the composition fields of the rocks of magmatic formations showed that this series is most similar to the alkali-earth series of rocks. The mineralogical compositions of cumulates and phenocrysts found in the effusive and dike varieties of these rocks correspond to unique sets of subsolidus phase associations and individual subsolidus phases crystallizing in this fundamental eutectic series.     

Cluster–subcluster mergers and the formation of narrow-angle tailed radio sources

We examine the ROSAT PSPC X-ray properties of a sample of 15 Abell clusters containing 23 narrow-angle tailed (NAT) radio galaxies. We find that clusters with NATs show a significantly higher level of substructure than a similar sample of radio-quiet clusters, indicating that NAT radio sources are preferentially located in dynamically complex systems. Also, the velocity distribution of the NAT galaxies is similar to that of other cluster members; these velocities are inadequate for producing the ram pressure necessary to bend the radio jets. We therefore propose a new model for NAT formation, in which NATs are associated with dynamically complex clusters undergoing merger events. The U -shaped NAT morphology is produced in part by the merger-induced bulk motion of the ICM bending the jets.     

Variations of global water exchange under changing climate

Variations of Global Sea Level are considered as an integral indicator of global water exchange. The results of analysis of Global Sea Level variations over past 140 years are estimated from tide-gauge data. Level trend in the XX century is shown to amount to 1.8 mm/year. The contributions of various factors to the formation of Global Sea Level trend are discussed. The interannual variations of evaporation and precipitation over the World Ocean are estimated for the first time, and their difference is shown to significantly contribute to the level trend, especially in the recent decade. Moreover, the significant rise in Global Sea Level is associated with the thermosteric level variations and, possibly, with the bottom melting of Antarctic shelf glaciers.     

Simulating future Caspian sea level changes using regional climate model outputs

We report on simulations of present-day climate (1961–1990) and future climate conditions (2071–2100, Special Report on Emissions Scenario A2) over the Caspian sea basin with a regional climate model (RCM) nested in time-slice general circulation model (GCM) simulations. We also calculate changes (A2 scenario minus present-day) in Caspian sea level (CSL) in response to changes in the simulated hydrologic budget of the basin. For the present-day run, both the GCM and RCM show a good performance in reproducing the water budget of the basin and the magnitude of multi-decadal changes in CSL. Compared to present-day climate, in the A2 scenario experiment we find an increase in cold season precipitation and an increase in temperature and evaporation, both over land and over the Caspian sea. We also find a large decrease of CSL in the A2 scenario run compared to the present-day run. This is due to increased evaporation loss from the basin (particularly over the sea) exceeding increased cold season precipitation over the basin. Our results suggest that the CSL might undergo large changes under future climate change, leading to potentially devastating consequences for the economy and environment of the region.