Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method of stabilization, of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Lyapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.This paper was supported by the National Research Council and the National Aeronautics and Space Administration and also by the Deutsche Forschungsgemeinschaft. It was presented at the Flight Mechanics/Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, Md., April 15–16, 1975.     

Neoproterozoic/Lower Palaeozoic Events in Central Dronning Maud Land (East Antarctica)

New geochronological data indicate that central Dronning Maud Land in East Antarctica underwent polyphase Neoproterozoic/Lower Palaeozoic metamorphism that can be correlated with the final amalgamation of E- and W-Gondwana. Central Dronning Maud Land most probably represents part of the southern continuation of the Mozambique Belt into E-Antarctica. The Neoproterozoic/Lower Palaeozoic metamorphism is preceded by a period of anorogenic anorthosite-charnockite magmatism at ca. 600 Ma. Polyphase metamorphism is recorded from ca. 580 to 515 Ma. Voluminous syntectonic magmatism has been documented at ca. 530 Ma, which is probably the most voluminous Neoproterozoic/Lower Palaeozoic syntectonic magmatism so far recorded in E-Antarctica. The Neoproterozoic/Lower Palaeozoic structural evolution evolved in an overall sinistral transpressional setting, and thus can be correlated with the broad tectonic setting of the Mozambique Belt in Africa.     

Shell architecture,element composition,and stable isotope signature of the giant deep-sea oyster Neopycnodonte zibrowii sp. n. from the NE Atlantic

A conspicuous new deep-sea oyster, Neopycnodonte zibrowii sp. n., is described from the Azores Archipelago, where it thrives in 420 to >500 m water depth in high densities concealed underneath overhangs. The new species reaches a relatively large size, which may exceed 20 cm, and is characterised by a very unusual hinge line morphology, straight without a bulge of the resilium. It is compared to the extant Indo-Pacific Empressostrea kostini Huber and Lorenz, 2007 and to the cosmopolitan Neopycnodonte cochlear (Poli, 1791), which has a broadly sympatric distribution at shallower depths in the Azores and Bay of Biscay. Radiocarbon dating reveals that individuals reach an impressive lifespan of one to more than five centuries, placing them among the longest-lived molluscs known to date. They often grow on top of each other, forming stacks that resemble dish piles—an effective measure to optimise shell stability with minimal biomineralisation effort, but with the drawback of increased bioerosion ultimately leading to detachment.Three microstructure types are developed in N. zibrowii: (1) the cross-foliated, calcitic, dorsal to central endostracum and aragonitic ligostracum, (2) the porous vesicular structure of the calcitic ventral endostracum, and (3) the simple prismatic aragonitic myostracum. Foliated and vesicular shell portions show sub-millimetre-scale first-order increments delineated by conchiolin-rich growth breaks (interpreted as reproductive cyclicity), and less distinct second-order increments (interpreted as annual in nature). This pattern is clearly reflected by the elemental composition with the primary growth breaks lacking Ca and Sr but including Mg and S as organic matrix constituents. The second-order increments within the calcite are mirrored by moderately co-varying Mg/Ca and S/Ca fluctuations at stable Sr concentrations, reflecting varying proportions of organic matrix. Dorsal and central endostracum transects reveal a low inter-valve, but considerable inter-specimen variability with high Mg/Ca molar ratios and fluctuations (22.5±17.6 mmol/mol), low Sr/Ca values (0.2±0.1 mmol/mol), and a typical to high S/Ca content (6.9±2.2 mmol/mol), when compared to other calcitic bivalves.Unlike short-lived, shallow-water oysters, N. zibrowii thrives under very stable environmental conditions. Minimal temperature fluctuations and stable open marine salinity provide an optimal basis to recognise biological fractionation processes. Strong Mg/Ca fluctuations indicate a physiological control related to metabolism and biomineralisation, prohibiting the use of this ratio as a temperature or ocean chemistry proxy. Low Sr/Ca ratios indicate rather constant and low long-term accretion rates, while short-scale fluctuations may be attributed to short-term variations in growth rate and Mg incorporation. Oxygen isotopes yield a considerable spread of 1.8‰ with a mean of 2.0±0.3‰ δ¹⁸O V-PDB, and low correlation between different contemporaneous parts of the shell and between specimens. These values surprisingly exceed expected equilibrium conditions, calculated from in situ temperature data (annual mean 12.3±0.3 °C) and seawater isotopic composition (0.5±0.1‰ δ¹⁸O SMOW), by 0.5‰ on average. Such positively shifting vital effects, previously reported for limpets and barnacles, are often overlooked in high-temperature and high-amplitude settings and may be more common than is currently believed. Carbon isotopes range from 0.2 to 3.5‰ δ¹³C V-PDB (mean 1.8±0.7‰) and show an ontogenetic decrease, but may incorporate an environmental signal in adult portions, indicated by a strong correspondence of peaks between specimens. This signal is likely driven by a complex interplay of different factors, such as primary production, current-based food supply and metabolism.     

Origin of Mercury’s double magnetopause: 3D hybrid simulation study with A.I.K.E.F.

During the first and second Mercury flyby the MESSENGER spacecraft detected a dawn side double-current sheet inside the Hermean magnetosphere that was labeled the “double magnetopause” (Slavin, J.A. et al. [2008]. Science 321, 85). This double current sheet confines a region of decreased magnetic field that is referred to as Mercury’s “dayside boundary layer” (Anderson, M., Slavin, J., Horth, H. [2011]. Planet. Space Sci.). Up to the present day the double current sheet, the boundary layer and the key processes leading to their formation are not well understood. In order to advance the understanding of this region we have carried out self-consistent plasma simulations of the Hermean magnetosphere by means of the hybrid simulation code A.I.K.E.F. (Müller, J., Simon, S., Motschmann, U., Schüle, J., Glassmeier, K., Pringle, G.J. [2011]. Comput. Phys. Commun. 182, 946–966). Magnetic field and plasma results are in excellent agreement with the MESSENGER observations. In contrast to former speculations our results prove this double current sheet may exist in a pure solar wind hydrogen plasma, i.e. in the absence of any exospheric ions like sodium. Both currents are similar in orientation but the outer is stronger in intensity. While the outer current sheet can be considered the “classical” magnetopause, the inner current sheet between the magnetopause and Mercury’s surface reveals to be sustained by a diamagnetic current that originates from proton pressure gradients at Mercury’s inner magnetosphere. The pressure gradients in turn exist due to protons that are trapped on closed magnetic field lines and mirrored between north and south pole. Both, the dayside and nightside diamagnetic decreases that have been observed during the MESSENGER mission show to be direct consequences of this diamagnetic current that we label Mercury’s “boundary-layer-current“.     

Paleogeographic and paleotopographic evolution of the Swiss and Eastern Alps since the Oligocene

The Alps are representing the most prominent topographic feature of central Europe in the last 30 Million years. Integration of sediment budget and thermochronological data show that crustal blocks within the Swiss and Eastern Alps experienced differential erosion and uplift, with eastward decreasing rates. Since 30 Ma, in the course of collision and slab breakoff, the Swiss and western Eastern Alps were uplifted and formed a mountain range. Moderate erosion rates stabilized  2 Myr later after adaption to the new base level. Between 28 Ma and 5 Ma, erosion rates shifted above and below different regional mean levels. These shifts of erosion rates were governed by changes of the tectonic setting. Moderate temporary drops of erosion rates and lowering of topography occurred at  21 Ma and  15 Ma in the course of lateral extension. Temporary rises occurred between 24 and 22 Ma during thrust loading and between 18 and 16 Ma during axial updoming of core complexes. By 5 Ma, a sustainable strong increase of erosion rates occurred in the Swiss and Western Alps. A much weaker increase is detected in the Eastern Alps somewhat later, which makes a tectonic trigger, probably a 2nd slab breakoff, more reasonable than a climatic trigger. However, this controversial 5-Ma event is superimposed by accelerated erosion after 2.7 Ma, governed by the onset of cyclic glaciations. Effective valley incision and sediment evacuation by glacial erosion caused isostatic compensation and pronounced young uplift of the Alps.The post-Eocene paleotopographic evolution of key areas is indirectly assessed on the base of erosion rates. Spatial change of paleotopography of the Alps and central Europe is estimated and illustrated in 3 paleogeographic maps.     

The graininess of dark matter haloes

We use the recently completed one billion particle Via Lactea II Λ cold dark matter simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as the structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions, the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo cannot be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function.     

Multimass spherical structure models for N-body simulations

We present a simple and efficient method to set up spherical structure models for N -body simulations with a multimass technique. This technique reduces by a substantial factor the computer run time needed in order to resolve a given scale as compared to single-mass models. It therefore allows to resolve smaller scales in N -body simulations for a given computer run time. Here, we present several models with an effective resolution of up to  1.68 × 10⁹  particles within their virial radius which are stable over cosmologically relevant time-scales. As an application, we confirm the theoretical prediction by Dehnen that in mergers of collisionless structures like dark matter haloes always the cusp of the steepest progenitor is preserved. We model each merger progenitor with an effective number of particles of approximately 10⁸ particles. We also find that in a core–core merger the central density approximately doubles whereas in the cusp–cusp case the central density only increases by approximately 50 per cent. This may suggest that the central regions of flat structures are better protected and get less energy input through the merger process.     

对气候变化背景下中欧易北河流域可用水的评估

The Elbe region is representative of humid to semi-humid landscapes in Central Europe,where water availability during the summer season is the limiting factor for plant growth and crop yields.especially in the loess areas with high crop productivity having annual precipitation lower than 500 mm.This paper summarizes the results of the first phase of the GLOWA(GLObal WAter)-Elbe project and tries to assess the reliability of water supply in the German part of the Elbe river basin for the next 50 years,a time scale relevant for the implementation of water and land use management plans.One focus of the study was developing scenarios which are consistent with climate and land use changes considering possible uncertainties.The concluding result of the study is that nature and communities in parts of Central Europe will have to deal with considerably lower water resources under scenario conditions.     

Supercooled diopside melt: confirmation of temperature-dependent expansivity using container-based dilatometry

The expansivity of supercooled diopside liquid has been determined using techniques of container-based dilatometry. Two thermal strategies have been employed, one in which the sample is brought to volumetric equilibrium by long-duration dwells at low temperatures (817 °C) and one in which scanning dilatometry of the sample has been performed at somewhat higher temperatures (890–913 °C). The results of both experiments yield a supercooled liquid expansivity for diopside liquid in the temperature range of 817–913 °C of 84.4 ± 2.8 × 10⁻⁴ cm³/mol K. The expansivity is 65% higher than that obtained for diopside melt obtained at superliquidus temperatures using the double bob Archimedean method. Combined fitting of the new low temperature, volume–temperature data from the present study and the superliquidus data from the literature has been performed. The combined fit yields the following equations for the volume–temperature relationship of diopside liquid (T=temperature in °C):