A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

Commentary and critique of “accounting for mineral resources: Issues and BEA's initial estimates”

The Bureau of Economic Analysis (BEA), U.S. Department of Commerce, in keeping with broad international efforts to green national gross domestic product (GDP) accounts, has attempted to create satellite accounts for mineral depletion. The present paper criticizes the BEA's unit rent measure of resource depletion, which is based upon Hotelling's pure theory of exhaustion. Following a thorough criticism of Hotelling's theory as a real-world model of mineral prices, practical issues related to the treatment of recycling, exploration, definition of reserves/resources, and their valuation/exploitation are introduced. For crude oil and natural gas and the nonfuel minerals, specific application problems of joint products and residuals complicate BEA's assumptions and efforts.     

Effects of water on strength and failure mode of coarse-grained granites at 300°C

Summary Deformation experiments have been performed in a triaxial compression cell at a temperature of 300°C and confining pressures up to 65 MPa using samples of homogeneous, fresh two-mica-granite (RM) and monzogranite (CM). The cylindrical specimens (d=70 mm, h=140 mm, V=540 cm³) were tested undrained under dry (105°C), as received, and water saturated conditions at deformation rates between and . The mechanical behaviour of the two types of coarse-grained, crystalloblastic granites is critically influenced by mineralogical composition, porosity, and the amount of intergranular water present in the samples. The failure stress of the CM granite is at about 65% of that of the RM granite; in both rocks strength decreases with increasing porosity and water content.The presence of interstitial water causes a failure mode of non-localized, homogeneously distributed microcracking in the central parts of the samples, whereas, in runs with dry granites, strain localization along a single shear fracture was observed. When aqueous fluids are present, the macroscopic style of deformation of granites appears to be ductile even at lowP andT conditions. Strength and angle of internal friction are reduced to very low values. The style of deformation, as well as the reduction of strength of the water-saturated rock samples, is due to mechanical and chemical effects of intergranular water at elevated temperatures.The maximum differential stresses measured for these coarse-grained granites are much lower than the strength commonly reported for other granites, e. g. Westerly and Charcoal granites. Our data suggest that the strength of the granitic crust under differential stress is lower than currently deduced from laboratory experiments.     

Cordierite-garnet-sillimanite-quartz equilibrium: I. New experimental calibration in the system FeO−Al2O3−SiO2−H2O and certain P-T-X H2O relations

The equilibrium in which hydrous Fe-cordierite breaks down to almandine, sillimanite, quartz, and water was previously experimentally determined by Richardson (1968) and Holdaway and Lee (1977) using QMF buffer and by Weisbrod (1973) using QIF buffer. All these studies yielded similar results — a negative dP/dT slope for the equilibrium curve. However, based on theoretical arguments, Martignole and Sisi (1981), and based on Fe-Mg partitioning experiments on coexisting cordierite and garnet in equilibrium with sillimanite and quartz, Aranovich and Podlesskii (1983) suggested that this equilibrium curve has a positive dP/dT slope and its position depends on the water content of the equilibrium cordierite. We have redetermined this equilibrium using a much improved tecnique of detecting reaction direction, and cordierite starting material that contained virtually no hercynite. Hercynite was present as a contaminant in the cordierites of previous experimental studies and possibly reacted with quartz during the experimental runs to expand the apparent stability field of Fe-cordierite. We synthesized Fe-cordierite from reagent grade oxides at 710°C and 2 kbar (using QMF buffer) with two intermediate stages of grinding and mixing. The cordierite has a unit cell volume of 1574.60 ų (molar volume=23.706 J/bar) and no Fe³⁺ as indicated by X-ray diffraction and room temperature Mössbauer studies respectively. Reaction direction was concluded by noting20% change of the ratios of intensities of two key X-ray diffraction peaks of cordierite and almandine. Our results show that the four-phase equilibrium curve passes through the points 2.1 kbar, 650°C and 2.5 kbar, 750°C. This disagrees with all previous experimental studies. H₂O in the Fe-cordierite, equilibrated at 2.2 kbar and 700°C and determined by H-extraction line in the stable isotope laboratory, is 1.13 wt% (n=0.41 moles). H₂O content of pure Mg-cordierite equilibrated under identical conditions and determined by thermogravimentric conditions and determined by thermogravimetric analysis is 1.22 wt% (n=0.40). Similar determinations on Fe-cordierite and Mg-cordierite equilibrated at 2.0 kbar and 650°C show 1.27 wt% (n=0.46) and 1.47 wt% (n=0.48) of H₂O respectively. Thus, H₂O content appears to be independent of Fe/Mg ratio in cordierite, a conclusion which supports previous experimental determinations. The experimentally determined equilibrium curve represents conditions of P_H2O=P_total. From this we calculated the anhydrous curve representing equilibrium under conditions of X _H2O ^V =0.0. A family of calculated equilibrium curves of constant n _H2O ^Cord cut the experimentally determined curve at a very small angle indicating a slight variation in n _H2O ^Cord in cordierite in equilibrium with almandine, sillimanite, and quartz under the conditions of constant X _H2O ^V . Ancther set of calculated equilibrium curves, each representing constant a _H2O ^V demonstrate that the slopes of the curves vary with X _H2O ^V , and are all positive in the full range of 0.0X _H2O ^V 1.0.     

Early Cretaceous volcaniclastic and quartzose sandstones from north central Nepal: composition,sedimentology and geotectonic significance

Early Cretaceous sandstones and shales from the Thakkhola region (Chukh and Tangbe Formations) were deposited on the subsiding northern (Tethyan) margin of Gondwana; current directions indicate a source area to the south. Whereas the Berriasian Chukh Formation is dominated by quartz arenites, volcaniclastic sandstones and minor conglomerates dominate the Tangbe Formation of Valanginian to Aptian age. Upsection, the composition of the volcaniclastic components changes from mainly basaltic to dominantly dacitic/rhyolitic. Magmatism was preceded and accompanied by strong uplift in the source area of the Chukh and Tangbe clastics, resulting in the erosion of probably more than several hundred meters of pre-Cretaceous sedimentary, metamorphic and plutonic rocks. A geochemical whole rock analysis of basaltic pebble fragments shows their alkaline character and suggests a within-plate geotectonic setting for the volcanic source. This volcanotectonic event is probably related to rifting between Australia and Greater India, where seafloor spreading began in late Valanginian/Hauterivian times.     

Fossil carotenoids and paleolimnology of meromictic Mahoney Lake,British Columbia,Canada

Vertical distribution of fossil carotenoids in a sediment core from meromictic Mahoney Lake was studied. Besides okenone and demethylated okenone, lutein and zeaxanthin and-carotene isomers were identified. No carotenoids typical for purple nonsulfur or green sulfur bacteria were detected. The ratio of zeaxanthin to lutein (above 1:1 in all samples) indicates a dominance of cyanobacteria over green algae in the phytoplankton assemblages of the past. Okenone, which is found exclusively in Chromatiaceae, was the dominating carotenoid in all sediment zones.The oldest sediment layers containing okenone were deposited 11 000 years ago. Between 9000 and 7000 and since 3000 years b.p., Chromatiaceae reached a considerable biomass in the lake. Vertical changes in okenone concentration were not related to changes of paleotemperatures. In contrast, okenone concentrations decreased during periods of volcanic ash input. During most of the lake history, however, mean okenone concentrations were positively correlated with sedimentation rates. This indicates that vertical changes of okenone concentration in the sediment reflect past changes of purple sulfur bacterial biomass in the lake.According to these results, the past limnology of Mahoney Lake resembled that of the present with a sulfide-containing monimolimnion and a well-developed population of okenone-bearing purple sulfur bacteria.     

Synthetic zeolites formed from expanded perlite: Type,formation conditions and properties

Summary The starting material used was expanded perlite with a grain size < 40 m (74.5 wt.% SiO₂; 12.5 wt.% Al₂O₃). This material is a waste product obtained during the production of expanded perlite. The experiments were carried out with KOH solutions, mixtures of KOH and NaOH solutions (1:1) as well as NaOH solutions in the concentration range 0.5 N to 6.0 N at temperatures of between 100° and 140°C and with reaction periods of 2 hours to 13 days in closed system. In the experiments with KOH containing solutions zeolite ZK-19 (phillipsite), W (merlinoite), G (chabazite) and F (edingtonite) formed. Without addition of aluminium high percentages of zeolite ZK-19 (80–100 wt.%) and zeolite W (90–100 wt.%) were obtained. The addition of aluminium rendered possibly the formation of 90 to 100 wt.% of zeolite G and 85 to 100 wt.% of zeolite F, respectively. In the experiments with NaOH solutions analcime, zeolite Na-Pc (gismondine), zeolite HS (sodalite hydrate) and zeolite A formed. High percentages of zeolite Na-Pc (90–100 wt.%), zeolite HS (up to 100 wt.%) and analcime (up to 100 wt.%) were synthesized without addition of aluminium. The formation of high percentages of zeolite A (95–100 wt.%), however, needs the addition of aluminium, NaCI and seed crystals. The temperature stability of the zeolites decreases in the following sequence: K-F > K-W K-ZK-19 (Na), K-W Na, K-F G_si-rich (Na), K-ZK-19 >> Na-Pc G_si-poor. Zeolite A has a very good temperature stability up to temperatures of } 550 °C similar to that of zeolite K-W. At higher temperatures, however, its stability is very poor. The NH₄ ⁺-exchange capacities (meq/g) of the different zeolites amount to the following values: ZK-19:2.8 - 3.2; W:3.0 - 3.2; G:2.3 - 3.6; A:3.1 - 3.2; Na-Pc:3.5 - 3.6; F : 3.9 - 4.8.

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Zeolithsynthese aus Blähperlit—Art, Bildungsbedingungen und Eigenschaften

Zusammenfassung Ausgangsmaterial der experimentellen Untersuchungen war Blähperlit mit einer Korngröße < 40 ,m (74,5 Gew.-% SiO₂; 12,5 Gew.-% Al₂O₃). Dieses Material ist ein Abfallprodukt, das bei der Produktion von Blähperlit anfällt. Die Experimente wurden mit KOH-Lösungen, Lösungsgemischen aus KOH und NaOH (1:1) sowie mit NaOH-Losungen im Konzentrationsbereich 0,5 n-6,0 n bei Temperaturen von 100° – 140°C und über Reaktionszeiten von 2 Stunden bis zu 13 Tagen im geschlossenen System durchgeführt. In den Experimenten mit KOH-hältigen Lösungen bildeten sich die Zeolithe ZK-19 (Phillipsit), W (Merlinoit), G (Chabasit) und F (Edingtonit). Hohe Prozentgehalte an Zeolith ZK-19 (80 – 100 Gew.-%) und Zeolith W (90–100 Gew.-%) entstehen nur ohne Zugabe von Aluminium. Die Bildung von 90–100 Gew.-% Zeolith G bzw. 85–100 Gew. % Zeolith F ist dagegen durch die Zugabe von Aluminium möglich. In den Experimenten mit NaOH-Lösungen bildeten sich die Zeolithe Analcim, Na-Pc (Gismondin), HS (Sodalithhydrat) und Zeolith A. Hohe Prozentanteile an Zeolith Na-Pc (90–100 Gew.-%), HS (bis zu 100 Gew. %) und Analcim (bis zu 100 Gew.-%) wurden ohne Aluminium-Zugabe synthetisiert. Die Bildung von hohen Gehalten an Zeolith A (95–100 Gew. %) ist jedoch nur unter Zugabe von Aluminium, NaCl und Kristallkeimen möglich.Die Temperaturbeständigkeit der Zeolithe nimmt in der folgenden Reihenfolge ab: K-F > K-W - K-ZK-19 (Na), K-W Na, K-F G_si-reich (Na), K-ZK-19 >> Na-Pc G_si-am. Zeolith A weist bis zu Temperaturen von etwa 550°C eine gute Temperaturbeständigkeit auf, die in etwa der von Zeolith K-W entspricht. Bei höheren Temperaturen ist die Beständigkeit jedoch sehr gering.Die NH⁴⁺-Austauschkapazitäten (mÄqu/g) der verschiedenen Zeolithe erreichen folgende Werte: ZK-19:2,8 - 3,2; W:3,0 - 3,2; G:2,3 - 3,6; A:3,1 - 3,2; Na-Pc:3,5 -3,6; F:3,9 - 4,8.

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With 2 Figures     

Die Rheingrabenrandverwerfung im Wattkopftunnel bei Ettlingen (Nordschwarzwald)

The Wattkopftunnel, near Ettlingen (Nordschwarzwald), drives through the eastern margin of the Rheingraben. The tunnel passes cenozoic and mesozoic sediments. Early quarternary and tertiary beds are situated west of the main thrust of the Rheingraben. Fossil record indicates upper Oligocene age (Chatt) for parts of the tertiary sediments. At the eastern border of the Rheingraben, wedges of jurassic and middle triassic series are squeezed. East of the Rheingraben the tunnel drives in the lower triassic Bausandstein. The eastern margin of the Rheingraben was investigated in detail during tunneling. Faults of the Rheingraben margin are distributed in an 130 meter wide fault zone in the tunnel. Total stratigraphic separation by the normal faults reaches more than 2 000 meters. The cenozoic sequence suffered synsedimentary to early diagenetic deformation, while the mesozoic series are characterized by ruptural deformation. The fault- and joint system is directed in the rheinische Richtung (SSW-NNE). East of the Rheingraben a second direction occur, running parallel to the lower Albtal (W-E).

     

Palaeoclimatic studies in South Shetland Islands,Antarctica, based on numerous stratigraphic variables in lake sediments

The hitherto longest found lake sediment sequence on Byers Peninsula, Livingston Island, South Shetland Islands, was analysed with respect to lithology, chronology, diatoms, Pediastrum, pollen and spores, mosses, mineralogy, and sediment chemistry. During the ca. 5000 year long development the sediments were influenced by frequent tephra fall-outs. This volcanic impact played a major role in the lake's history during two periods, 4700–4600 and 2800–2500 BP, but was of importance during the lake's entire history with considerable influence on many of the palaeoenvironmentally significant indicators. The large and complex data set was analysed and zonated with different types of multivariate analysis. This resulted in a subdivision of the sequence into 8 time periods and 21 variables. Redundancy analysis (RDA) of this data set, both without and with the tephra periods, and with 4–6 of the variables as explanatory environmental variables, reveal that climatic/environmental signals are detectable. The palaeoclimatic picture that emerged out of the tephra noise suggests that the first 100 years were characterized by mild, humid conditions. This was followed by a less mild and humid climate until ca. 4000 BP when a gradual warming seems to have started, coupled with increased humidity. These mild and humid conditions seem to have reached an optimum slightly after 3000 BP. At ca. 2500 BP a distinct climatic deterioration occurred with colder and drier conditions and long seasons with ice cover. This arid, cold phase probably reached its optimum conditions at ca. 1500 BP, when slightly warmer conditions might have prevailed for a while. Except for the modern sample with rather mild climate, the last 1400 years seem to have been fairly arid and cold, and the effects of the frequent volcanic activity during this period is only vaguely seen in the records.     

High-resolution sequence stratigraphy of the Lower Triassic ‘Buntsandstein’ in the Netherlands and northwestern Germany

Detailed log correlations of the largely fluvio-lacustrine Lower Triassic Buntsandstein (Late Permian-Early Anisian), carried out on 80 wells in the Dutch onshore and offshore areas, can be linked to northwest-German high-resolution sequence stratigraphy. The correlations show that cyclic sedimentation occurred in large parts of the basin. Seven 1st-order sequences are recognised, namely the Main Claystone, Rogenstein, Volpriehausen, Detfurth, Hardegsen, Solling and Lower Röt Sequences. They are overlain by the lower part of the Upper Röt–Lower Muschelkalk Sequence. Distinct sequence boundaries have been identified at the bases of four sequences: Volpriehausen, Detfurth, Solling and Upper Röt. The higher-order sequences consist of fining-upwards cycles with a thickness of up to tens of metres. The sequences are laterally persistent and have a characteristic expression on gamma-ray and sonic logs. In the Lower Buntsandstein, they display a uniform character throughout most of the area, with only minor differences in thickness or lithology. NNE-oriented lows and swells were formed during deposition of the Volpriehausen, Detfurth and Hardegsen Sequences. Uplift prior to the deposition of the Solling Sequence caused deep erosion on the swells in the basin and minor erosion in the lows. The high-resolution sequences probably represent alternating, relatively wet and dry climatic periods, with a periodicity of about 100 000 years. An analysis of the sequences suggests that their reduced thickness on the swells is mainly the effect of erosion. This is supported by analyses of the accumulation patterns and rates.