Periodic orbits and their bifurcations in a 3-D system

We study some simple periodic orbits and their bifurcations in the Hamiltonian . We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (). In the regionsS andU there are lines of equal rotation numberm/n. Along these lines we have bifurcations of families of periodic orbits of multiplicityn. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region there are linesm/n, along which the orbits 1a, describedn-times, are doubly unstable; however, along these lines there are no bifurcations ofn-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (, ). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams.     

Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem

The non-linear stability of the libration pointL ₄ in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL ₄ is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:

On the electron density in an active region observed by SERTS

Emission lines from an active region, observed by SERTS, have been used to determine electron densities from theoretical curves for Mgvii, Siviii, and Siix density-sensitive line ratios. Density diagnostics of Alviii 285.46/323.52 line emissivity ratio has also been investigated.     

The near infrared camera on the W.M. Keck telescope

The near infrared camera (NIRC) was used for a science demonstration run on the Keck telescope during 16–24 March 1993. The camera used a 256×256 InSb array manufactured by Santa Barbara Research Corporation. Observations were obtained using narrowband and broad band filters from 1 to 2.4 microns, and grisms with a spectral resolution of 0.6 percent in the J, H and K atmospheric windows. The instrument was fully background limited over the entire wavelength range. The sky background was quite low, reaching 14.3 mag/square arc sec in the broadband K _s filter. The image quality of the camera + telescope was excellent, being seeing limited in the range 0.5–0.9.The science demonstration observations of the NIRC on the Keck Telescope included observations of the most distant galaxy known, 4C41.17 at a redshift z=3.8 and the most luminous object known, the IRAS source FSC10214+4724 at a redshift z=2.29. Observations of the radio galaxy address the problem of the alignment effect in high redshift radio galaxies as well as the environments of such systems. FSC10214+4724 appears to be a merging galaxy that is at least 5×10⁸ years old.Based on observations obtained at the W.M.Keck Observatory, which is operated jointly by the California Institute of Technology and the University of CaliforniaThe W.M. Keck Observatory is operated as a scientific partnership between the California Institute of Technology and the University of California. It was made possible by the generous gift of the W.M. Keck foundation and the support of its president, Howard Keck.     

Deposition and diagenesis of the lacustrine-fluvial Cangfanggou Group (uppermost Permian to Lower Triassic), southern Junggar Basin,NW China: a contribution from sequence stratigraphy

The Junggar Basin in NW China contains lacustrine hydrocarbon source rocks which are among the highest quality of hydrocarbon potential in the world. Oil reservoirs in the basin are very substantial: target reservoirs span Carboniferous to Tertiary strata and include Permo-Triassic lacustrine and fluvial sandstones. The Junggar Basin was a foreland basin during the late Permian to Cenozoic, possibly with strike-slip tectonics at the southern margin during Mesozoic time. The Cangfanggou Group, as one of the major reservoirs, is well-exposed in the eastern part of the southern Junggar Basin. A measured outcrop section and a number of borehole logs coupled with resistivity logs were used to attempt sequence stratigraphic analysis. Detailed sedimentological studies on the outcrops and borehole cores have demonstrated that the Cangfanggou Group is characterized by alternating lacustrine and fluvial deposits. Four depositional sequences have been recognized. For each sequence, the basal boundary is marked by erosional truncation of fluvial channel conglomeratic sandstones in sharp contact with underlying lacustrine or floodplain mudstones. The top of each lowstand systems tract is normally overlain by the transition to lacustrine or maximum flooding surface. The transgressive systems tract is normally not identifiable at the basin margin, but was developed in the basinward area and characterized by interbedded fining-upward distal fluvial and shallow lacustrine deposits. The highstand systems tract at the basin margin is characterized by very thick floodplain mudstones or shallow lacustrine deposits, and by typical coarsening-upward parasequences of shallow lacustrine deposits in more basinward areas. Sediment input to the basin was controlled by tectonics and climate. Depositional sequences were probably controlled by fluctuating change of lake level: this was in turn controlled by climate (runoff), modified by tectonics in specific areas.The sandstones studied are exclusively volcanic litharenites. Diagenetic studies suggest that the calcite cementation, pore-filling clay minerals and zeolites occluded substantial porosity in the sandstones examined because they are compositionally immature. However, notable secondary porosity in varying proportions is present in the sandstones of the Cangfanggou Group, resulting from the dissolution of unstable detrital grains. The lowstand fluvial/distal fluvial sandstones recorded the highest average porosity and highest permeability, in which some primary porosity may remain because early formed clay coatings inhibited further compaction. The combination of residual primary porosity and significant amount of secondary porosity in the sandstones of the Cangfanggou Group may constitute moderate to good reservoirs. In contrast, the lacustrine fine-grained sandstones is characterized by clay authigenesis and zeolitization, in which the porosity was obliterated by the zeolites and extensive illitization; the lowstand fluvial channel sandstones in the basin margin areas are characterized by extensive calcite cementation which greatly reduced the porosity and permeability.This is the fifth paper in a series of papers published in this issue on Climatic and Tectonic Rhythms in Lake Deposits.     

A verification of some methods to determine the fluxes of momentum,sensible heat,and water vapour using standard deviation and structure parameter of scalar meteorological quantities

A set of micro-meteorological data collected over a horizontal, uniform terrain (the plain of La Crau, France) in June 1987 is analysed. Conditions were predominantly sunny and arid, while due to the Mistral the wind speed could exceed 10 m/s. Verification of several methods to evaluate surface fluxes of heat, momentum and water vapour from the standard deviation of temperature, wind and specific humidity is presented. Also, a similar approach using the structure parameter of temperature is considered. These methods are all based on Monin-Obukhov (M-O) similarity theory. It is found that the standard deviation of temperature, vertical and horizontal wind speed as well as the structure parameter for temperature behave according to M-O similarity. It is shown that the sensible heat flux and friction velocity can be determined from a fast response thermometer and a cup anemometer. Also, it appears that the analytic solution of the set of governing equations as derived by the first author yields good results. M-O theory does not appear to work for the standard deviation of specific humidity. This may be due to the relative importance of large eddies.     

Correlation methods in fingerprint detection studies

This investigation addresses two general issues regarding the role of pattern similarity statistics in greenhouse warming detection studies: normalization, and the relative merits of centered versus uncentered statistics. A pattern correlation statistic is used to search for the greenhouse warming signals predicted by five different models in the observed records of land and ocean surface temperature changes. Two forms of this statistic were computed: R (t), which makes use of nonnormalized data, and (t), which employs point-wise normalized data in order to focus the search on regions where the signal-to-noise ratio is large. While there are no trends in the R (t) time series, the time series of (t) show large positive trends. However, it is not possible to infer from the (t) results that the observed pattern of temperature change is, in fact, becoming increasingly similar to the model-predicted signal. This is because point-wise normalization of the observed and simulated mean change fields by a single common field introduces a common factor effect, which means that the quantities being compared should show some similarity a priori. This does not necessarily make normalization inapplicable, because the detection test involves seeking a trend in the similarity statistic. We show, however, that trends in (t) must arise almost completely from the observed data, and cannot be an indicator of increasing observed data/signal similarity. We also compare the information provided by centered statistics such as R(t) and the uncentered C(t) statistic introduced by Barnett. We show that C(t) may be expressed as the weighted sum of two terms, one proportional to R(t) and the other proportional to the observed spatial mean. For near-surface temperatures, the spatial average term dominates over the R(t) term. In this case the use of C(t) is equivalent to the use of spatial-mean temperature. We conclude that at present, the most informative pattern correlation statistic for detection purposes is R(t), the standard product-moment correlation coefficient between the observed and model fields. Our failure to find meaningful trends in R(t) may be due to the fact that the signal is being obscured by the background noise of natural variability, and/or because of incorrect model signals or sensitivities.     

Cu 2p absorption spectroscopy as a probe for the site occupancy of (ZnxCu1−x)WO4 solid solution

The solid solution sanmartinite (ZnWO₄)—cuproscheelite (CuWO₄) has been studied using Cu 2p X-ray absorption spectroscopy. While a single L₃ absorption peak is observed for CuWO₄, two distinct L₃ absorption peaks with a separation of ～0.8 eV are observed for the intermediate samples in the solid solution. The two peaks represent distinct Cu sites: one with all CuO₆ next nearest neighbours in the (Cu,Zn)O₆ chains, another having at least one ZnO₆ next nearest neighbour. Both sites show a linear increase in covalency as a function of increasing Cu-content. The relative intensities of the two absorption peaks is dependent upon the Cu-content and has been used to model the site occupancies. The results reveal that the local structural effects can be associated with a composition-dependent structural phase transition from P2/c (ZnWO₄) to P $\bar 1$ (CuWO₄). Deviations from a single-site model are explained in terms of the local environments, and evidence for site preferences and local clustering are explored.     

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     

Corona textures in Proterozoic olivine melanorites of the Equeefa Suite,Natal Metamorphic Province,South Africa

Summary Olivine-plagioclase and phlogopite-plagioclase coronas have been identified from olivine melanorites of the Mid- to Late Proterozoic Equeefa Suite in southern Natal, South Africa. Olivine, in contact with plagioclase, is mantled by a shell of clear orthopyroxene, in turn rimmed by pale green (pargasitic) clinoamphibole. Locally a third rim, composed of a fine pargasite-spinel symplectite is developed adjacent to the plagioclase. The second corona reaction has produced greenish-brown pargasite at phlogopite-plagioclase interfaces. A third, less obvious reaction, between olivine and phlogopite is also noted. Analytical data of all the mineral phases present, along with the coronas, are given. Two-pyroxene thermometry yields magmatic core temperatures ( 1120°C), with rim compositions indicating equilibration at 850°C. Consistent with this, the modelled olivine-plagioclase reaction occurs between 830–1050°C with a_waterbetween 0.1 and 1.0 at 7 kbar. The three reactions took place during a prolonged history of cooling and partial hydration of the magmatic olivine melanorites from over 1000°C down to 600°C. The P-T conditions indicated by the reactions suggest this cooling process was essentially isobaric, indicating that the area was not subjected to rapid uplift or burial throughout this entire period.

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Korona-Texturen in proterozoischen Olivin-Melanoriten der Equeefa Suite, Natal Metamorphic Province, Südafrika

Zusammenfassung Aus Olivin-Melanoriten der mittel- bis spätproterozoischen Equeefa Suite im südlichen Natal, Südafrika, wurden Olivin-Plagioklas und Phlogopit-Plagioklas-Koronartexturen beobachtet. Olivin, der mit Plagioklas im Kontakt steht, wird von einem klaren Saum vom Orthopyroxen ummantelt, der seinerseits von blaßgrünem (pargasitischem) Klinoamphibol umsäumt wird. Stellenweise ist ein dritter Saum, bestehend aus feinkörnigem symplektitischem Pargasit-Spinell im Kontakt mit Plagioklas ausgebildet. Die zweite koronabildende Reaktion resultiert in Bildung eines grünbraunen Pargasites an Phlogopit-Plagioklas Kornkontakten. Eine dritte, weniger auffällige Reaktion zwischen Olivin und Phlogopit wurde ebenfalls beobachtet. Zwei-Pyroxen-Thermometrie ergab magmatische Temperaturen der Kernbereiche ( 1120°C) und belegt eine Gleichgewichtseinstellung in den Randzonen bei ca. 850°C. Olivin-Plagioklas-Modellreaktionen liegen ebenfalls in einem Temperaturbereich von 830–1050°C bei Wasseraktivitäten von 0.1 bis 1.0 und einem Druck von 7 kbar. Die drei Reaktionen liefen im Zuge einer länger andauernden Abkühlung unter teilweiser Hydratisierung der magmatischen Melanorite in einem Temperaturbereich von 1000°C bis ca. 600°C ab. Die aus den Reaktionen ableitbaren P-T-Bedingungen sprechen für eine im wesentlichen isobare Abkhlungsgeschichte und zeigen, daß dieses Gebiet wáhrend dieser gesamten Periode keiner raschen Hebung bzw. keiner Versenkung unterworfen worden ist.