A High Order Perturbation Analysis of the Sitnikov Problem

The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré–Lindstedt. The enormous amount of necessary computations were performed by extensive use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering an increasing number of algebraic terms originating from high order perturbation theory.     

A comparison of a GCM response to historical anthropogenic land cover change and model sensitivity to uncertainty in present-day land cover representations

This study assesses the sensitivity of the fully coupled NCAR-DOE PCM to three different representations of present-day land cover, based on IPCC SRES land cover information. We conclude that there is significant model sensitivity to current land cover characterization, with an observed average global temperature range of 0.21 K between the simulations. Much larger contrasts (up to 5 K) are found on the regional scale; however, these changes are largely offsetting on the global scale. These results show that significant biases can be introduced when outside data sources are used to conduct anthropogenic land cover change experiments in GCMs that have been calibrated to their own representation of present-day land cover. We conclude that hybrid systems that combine the natural vegetation from the native GCM datasets combined with human land cover information from other sources are best for simulating such impacts. We also performed a prehuman simulation, which had a 0.39 K ~higher average global temperature and, perhaps of greater importance, temperature changes regionally of about 2 K. In this study, the larger regional changes coincide with large-scale agricultural areas. The initial cooling from energy balance changes appear to create feedbacks that intensify mid-latitude circulation features and weaken the summer monsoon circulation over Asia, leading to further cooling. From these results, we conclude that land cover change plays a significant role in anthropogenically forced climate change. Because these changes coincide with regions of the highest human population this climate impact could have a disproportionate impact on human systems. Therefore, it is important that land cover change be included in past and future climate change simulations.     

REE distribution in some layered migmatites: constraints on their petrogenesis

The REE distributions in mesosomes, neosomes, leucosomes and melanosomes of four layered migmatites have been investigated. In one example (Arvika migmatites) the REE patterns in adjacent paragneisses, the presumed parent rock of the migmatites, were also determined. REE patterns of neosomes and mesosomes of Arvika migmatites are similar to the finegrained layers and coarse-grained layers, respectively, observed in the adjacent paragneiss. This is in agreement with the layer-by-layer paragneiss-migmatite transformation model.

The REE patterns of mesosomes and neosomes indicate that these lithologies may have been closed systems (for REE) during the formation of the migmatites. No indication of metasomatic reactions, melt segregation or injection could be detected. Within the neosomes, leucosomes are depleted and melanosomes enriched in REE contents. This is interpreted to be due to separation and concentration of accessory minerals (monazite, epidote, allanite, zircon, sphene, apatite, garnet) into the melanosomes. The behaviour of accessory minerals during migmatite formation is closely allied to that of biotite, which is also concentrated in the melanosomes.     

Phase equilibria and compositions of Fe-Mg-Al minerals and melts in water-saturated peraluminous granitic systems

Phase assemblages and phase compositions were studied experimentally in water-saturated, biotite-bearing peraluminous granitic melts as a function of alumina excess and temperature. The runs were performed at 2 and 5 kbars under NNO buffer. Biotite was stable only in composition containing 5% of normative corundum; it coexisted with cordierite and hercynite at 2 kbars and with hercynite at 5 kbars. In composition containing 10% of normative corundum biotite was not observed; abundant cordierite and hercynite were the only Fe-Mg-Al minerals. These relationships show that, at constant pressure, the amount of cordierite increases with increasing excess of alumina. Simultaneously the stability of biotite decreases due to preferential partitioning of Mg into cordierite and Fe into biotite. Besides the distribution of Fe, Mg and Al among the coexisting solid phases, solubility of these elements in the melts is given. Below 900° C melts are poor in iron and magnesium and correspond, in terms of these elements, to leucogranites. It is suggested that the leucogranitic magmas, such as parental magmas of European Hercynian and Himalayan leucogranites, must have been formed through highly efficient separation of partial melt from restite, in which ferromagnesian components are concentrated. Peraluminous granites rich in ferromagnesian minerals originate supposedly from restite-bearing magmas.     

Eclogite-facies vein systems in the Marun-Keu complex (Polar Urals,Russia): textural,chemical and thermal constraints for patterns of fluid flow in the lower crust

Metasomatic amphibole-eclogite sequences grew in selvages of quartz veins from the Marun-Keu complex (Polar Urals, Russia) during high-pressure metamorphism. Relicts of a pre-metasomatic eclogite-facies assemblage are present in the wallrock layers as irregular patches. Wallrock interstitial quartz trails lying at a high angle to reaction fronts provide evidence for grain-scale pore channelisation which may be produced by intergranular-fluid compositional gradients parallel to the quartz trails. Disequilibrium at vein-wallrock scale is inferred from wallrock mineral heterogeneity and from variable initial Sr isotope ratios in mineral separates. Mass-balance calculations between relicts and wallrock assemblages reveal chemical imbalances caused by open system-behaviour with two way mass-transfer. The vein-wallrock system registers a prograde history from 408–434 °C (relicts) to 526–668 °C (vein precipitates). Vein and metasomatic assemblages formed during a single fluid-rock interaction process, implying high heating rates (100 °C/Ma), which could result from heat advection by large-scale fluid circulation.Editorial responsibility: W. Schreyer