A generalization of Hopf's bifurcation problem

The topic presented here is not really a topic of celestial mechanics, because a dissipative system is considered, and dissipative systems do not occur in celestial mechanics at least if drag is not taken into account. Only in the theoretical background of Baumgarte-Stiefel stabilization dissipative systems become important. The only justification is that, in order to establish the result, a tool, namely the method of averaging, is used here which is a good tool for many problems of celestial mechanics too.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Some properties of velocity fields in the solar photosphere

Photoelectric records of the Doppler effect (DE) and longitudinal Zeeman effect (LZE) were obtained with the Capri magnetograph of the Fraunhofer Institut photoelectric, using the Fei line λ 5250.22. Each record consists of 65 scans repeated along the same line on the sun. The analysis of 16 records covering a total of 485 oscillating regions (period 300 sec) leads to the following results:

1. (1)
   The mean lifetime of the DE-oscillations outside active regions is 20 min and 32 min in the neighborhood of spotgroups. Discarding the weakest sporadic osculations, one obtains 27 min and 43 min respectively. The most frequent lifetime in both cases is 15 min.     

Mapping of lunar surface from side-looking orbital radar images

Side-looking spacecraft radar imagery has thus far been produced only from an orbit around the Moon. This was a part of the Apollo Lunar Sounder Experiment (ALSE) of the Apollo 17 mission in December, 1972. This paper reports results of a radargrammetric evaluation of overlapping Apollo 17 synthetic aperture radar images (wavelength 2 m). The potential to map from single images and to reconstruct 3D stereoscopic models is studied. The relative height accuracy achieved is about ± 100 m and is thus competitive with that obtained with the vidicon camera that is presently used for planetary exploration.NAS-NRC Resident Research Associate.     

1: Subduction, slab detachment and mineralization: The Neogene in the Apuseni Mountains and Carpathians

The Inner Carpathians comprise several distinct Neogene late-stage orogenic Pb–Zn–Cu–Ag–Au ore districts. The mineral deposits in these districts are closely related to volcanic and subvolcanic rocks, and represent mainly porphyry and epithermal vein deposits, which formed within short periods of time in each district. Here, we discuss possible geodynamic and structural controls that suggest why some of the Neogene volcanic districts within the Carpathians comprise abundant mineralization, while others are barren. The Neogene period has been characterized by an overall geodynamic regime of subduction, where primary roll-back of the subducted slab and secondary phenomena, like slab break-off and the development of slab windows, could have contributed to the evolution, location and type of volcanic activity. Structural features developing in the overlying lithosphere and visible in the Carpathian crust, such as transtensional wrench corridors, block rotation and relay structures due to extrusion tectonics, have probably acted in focusing hydrothermal activity. As a result of particular events in the geodynamic evolution and the development of specific structural features, mineralization formed during fluid channelling within transtensional wrench settings and during periods of extension related to block rotation.In the Slovakian ore district of the Western Carpathians, Neogene volcanism and associated mineralization were localized by sinistral, NE-trending wrench corridors, which formed part of the extruding Alcapa block. The Baia Mare ore district, in the Eastern Carpathians, reflects a transtensional wrench setting on distributed oversteps close to the termination of the Dragos Voda fault. There, mineralization was spatially controlled by the transtensional Dragos Voda master fault and associated cross-fault systems. The Golden Quadrangle Cu–Au ore district of the Southern Apuseni Mountains reflects an unusual rotated transtensional/extensional setting close to the termination of a graben system. There, fluid flow was probably localized by fault propagation at the inner tip of the graben system.The spatial and temporal evolution of the magmatism and its changing geochemical signature from (N)W to (S)E strongly suggests a link with the contemporaneous northeastward roll-back of the subducted slab and a progressive southeastward detachment during accelerating roll-back. This geodynamic evolution is further supported by the present-day overall and detailed mantle lithospheric density images, the present-day heat flow patterns, the crustal architecture and its interpreted evolution, and the spatial and temporal evolution of depocentres around the Carpathian arc. In contrast to all these features, the mineral deposits in the West Carpathians, East Carpathians and Apuseni Mountains are too synchronous with respect to their individual volcanic history and contrast too much with younger volcanics of similar style, but barren, in southeastern parts of the Carpathians to simply link them directly to the slab evolution. In all three districts, the presence of magmatic fluids released from shallow plutons and their mixing with meteoric water were critical for mineralization, requiring transtensional or extensional local regimes at the time of mineralization, possibly following initial compressional regimes.These three systems show that mineralization was probably controlled by the superposition of favourable mantle lithospheric conditions and partly independent, evolving upper crustal deformation conditions.In the 13 to 11 Ma period the dominant mineralization formed all across the Carpathians, and was superimposed on structurally favourable crustal areas with, at that time, volcanic–hydrothermal activity. The period may reflect the moment when the (upper part of the) crust failed under lithospheric extension imposed by the slab evolution. This crustal failure would have fragmented the overriding plate, possibly breaking up the thermal lid, to provoke intensive fluid flow in specific areas, and allowed subsequent accelerated tectonic development, block rotation and extrusion of a “family of sub-blocks” that are arbitrarily regarded as the Tisia–Dacia or Alcapa blocks, even though they have lost their internal entity.     

Spatial distribution of heavy metals in surficial sediments from Guanabara Bay: Rio de Janeiro, Brazil

Ninety-two surface sediment samples were collected in Guanabara Bay, one of the most prominent urban bays in SE Brazil, to investigate the spatial distribution of anthropogenic pollutants. The concentrations of heavy metals, organic carbon and particle size were examined in all samples. Large spatial variations of heavy metals and particle size were observed. The highest concentrations of heavy metals were found in the muddy sediments from the north western region of the bay near the main outlets of the most polluted rivers, municipal waste drainage systems and one of the major oil refineries. Another anomalous concentration of metals was found adjacent to Rio de Janeiro Harbour. The heavy metal concentrations decrease to the northeast, due to intact rivers and the mangrove systems in this area, and to the south where the sand fraction and open-marine processes dominate. The geochemical normalization of metal data to Li or Al has also demonstrated that the anthropogenic input of heavy metals have altered the natural sediment heavy metal distribution.     

Kinematics of the Inntal shear zone–sub-Tauern ramp fault system and the interpretation of the TRANSALP seismic section, Eastern Alps, Austria

A new interpretation of the Inntal–Tauern sector of the TRANSALP seismic section is presented. One of the most prominent contrasts in reflectivity in the TRANSALP seismic section is the contact between the Bajuvaric unit in the footwall and the overlying Tirolic unit and its basement across a moderately south-dipping interface. We trace this contact from the surface at the southern margin of the Inn valley to a depth of 5 km. There, the contact is deformed or cut by the Tauern Window northern margin. We define the contact between Bajuvaric and Tirolic units as Brixlegg thrust, which is older than Miocene Tauern window exhumation and has a Paleogene age. The sub-Tauern ramp connects with the Inntal fault system at the surface and roots below the Tauern window. Oblique thrust movements across this fault system in the Miocene caused exhumation of the hanging wall, where the fault has a ramp geometry, which is in the area of the TRANSALP cross section and west of it. East of the TRANSALP cross section, the fault system merges with Alpine basal thrust, which is a flat. No Miocene exhumation occurred above the flat.     

High-pressure phengite decomposition in the Weissenstein eclogite,Münchberger Gneiss Massif,Germany

The petrography, mineral chemistry and petrogenesis of a sample from the Weissenstein eclogite, Bavaria, Germany, has been investigated. The total mineral assemblage comprises garnet, clinopyroxene_I+II, quartz, amphibole_I+II, rutile, phengite, epidote/allanite, plagioclase, biotite, apatite, pumpellyite, titanite (sphene), zircon, alkali feldspar and calcite. Textural observations combined with geothermobarometry (Fe/Mg distribution between clinopyroxene/garnet and phengite/garnet; jadeite-content of omphacite, Si-content of phengite, and An-content of plagioclase) provide indications of two different stages in the metamorphic evolution of the rock. The main phengitequartz-eclogite mineral equilibration occurred at minimum P=13–17kbar, minimum T=620±50° C; the retrograde symplectite stage (clinopyroxene_II, amphibole_II, biotite, plagioclase) occurred at P _total between 12 and 8.5 kbar. Reactions of the symplectite stage are:

1. phengite (core) + Na₂O_aq + CaO_aq=phengite (rim) + biotite + plagioclase + K₂O_aq + H₂O
2. phengite (core) + clinopyroxene_I + Na₂O_aq=phengite (rim + biotite + plagioclase + amphibole_II + SiO₂ + K₂O_aq + CaO_aq + H₂O
3. clinopyroxene_I + SiO₂ + K₂O_aq + H₂O=clinopyroxene_II + plagioclase+amphibole_II + Na₂O_aq + CaO_aq

The phengite decomposition produces H₂O, whereas the clinopyroxene decomposition consumes H₂O. The estimated P-T-conditions for the Weissenstein eclogite are in the same order of magnitude as those for other eclogite bodies from the Alps and Caledonides believed to be related to subduction processes.     

P-T evolution of metasediments from the Eclogite Zone, south-central Tauern Window, Austria

Petrologic data on the paragenesis of (I) kyanite-zoisite marbles and (II) garnet-chloritoid quartz-mica schists are presented with the goal of providing constraints on the pressure-temperature evolution of the Eclogite Zone, Tauern Window, Austria. The peak metamorphic assemblages in the two rock types are: (I) kyanite + zoisite + dolomite + quartz; zoisite + muscovite + dolomite + calcite + quartz; and (II) garnet + chloritoid + kyanite + muscovite + quartz + epidote ± dolomite ± Zn-staurolite. The estimated peak metamorphic conditions are 19 ± 2 kbar, 590 ± 20°C.

Secondary alteration of the kyanite-zoisite marbles was accomplished in two stages. The early stage resulted in the production of margarite, paragonite, secondary muscovite and chlorite and the later stage resulted in the formation of sudoite (a di/trioctahedral Mg---Al layer silicate) and kaolinite. The early alteration is bracketed at conditions between 3 and 10 kbar, 450–550°C and the later alteration between 200 and 350°C, P 3 kbar.

The P-T path is characterized by maximum burial to approximately 19 kbar (60–70 km) (at≈590°C), followed by nearly isothermal decompression to approximately 10 kbar (30 km), and then more gradual decompression with cooling to approximately 3 kbar (10 km). Alteration was apparently accomplished by the influx of H₂O-rich fluids, with the composition of the fluid locally buffered by the mineral assemblage.     

Gewinnung biokinetischer Daten von Abwässern mit dem Respirationsfermentor. Teil 2: Einfluß des Sauerstoffpartialdruckes auf die spezifische Wachstumsrate beim aeroben biologischen Abbau von Prozeßwasser der Braunkohlenvergasung im mesophilen und im thermophilen Temperaturbereich

An improved laboratory respiration fermentor construction for batchwise operations by which permeations of gases through connecting rubber tubings could be avoided is described. From the registration of curves for oxygen consumption during batchwise treatment of waste water from coal gasification at 37°C a decrease of the COD reduction rate is observed when the dissolved oxygen concentration decreased to below 0,7 mg/l. At dissolved oxygen concentrations above 0,7 mg/l, biokinetic data were determined which on account of the improved respiratory fermenter construction diverge strongly from the values formerly given \documentclass{article}\pagestyle{empty}\begin{document}$({\rm \mu = 0,24 h}^{{\rm - 1}};Y_{\frac{x}{{{\rm O}_2 }}} = 0,57{\rm g\; OBTSZ/g O}_{\rm 2};Y_{\frac{x}{s}} = 0,32{\rm g\; OBTSZ/g\; COD}) $\end{document}. Investigations performed in the thermophilic range (55°C) led at dissolved oxygen concentration of 1,5 mg/l to significant slower COD-reduction rates whereas at dissolved oxygen concentration of 1,5 mg/l the efficiency of COD-reduction was significantly higher than in the mesophilic range. The results obtained at different dissolved oxygen concentrations and different treating temperatures are discussed.