The onset of chaotic motion in the restricted problem of three bodies

A full characterization of a nonintegrable dynamical system requires an investigation into the chaotic properties of that system. One such system, the restricted problem of three bodies, has been studied for over two centuries, yet few studies have examined the chaotic nature of some ot its trajectories. This paper examines and classifies the onset of chaotic motion in the restricted three-body problem through the use of Poincaré surfaces of section, Liapunov characteristic numbers, power spectral density analysis and a newly developed technique called numerical irreversibility. The chaotic motion is found to be intermittent and becomes first evident when the Jacobian constant is slightly higher thanC ₂.     

Geology of the volcanic-hosted Brockman rare-metals deposit,Halls Creek Mobile Zone,northwest Australia. l. Volcanic environment,geochronology and petrography of the Brockman volcanics

Summary Rare-metals mineralization of the Brockman deposit (Halls Creek Mobile Zone, NW Australia) is hosted in a fluorite-bearing, rhyolitic volcaniclastic unit informally termed the Niobium Tuff. The Tuff, more correctly described as a tuffaceous volcaniclastic deposit, is the lowermost unit of a sequence of trachyte-to-rhyolite lavas, trachyandesite subvolcanic rocks, and volcaniclastic units of the Brockman volcanics located within the Halls Creek Group, a thick, early Proterozoic volcano-sedimentary sequence. High precision SHRIMP ion-microprobe zircon dating of the Niobium Tuff gives an eruption age of 1870 ± 4 Ma. Regional geochronological constraints indicate the Niobium Tuff was deposited about 15 Ma before major orogenic activity affected the area. Despite folding, faulting and low-grade metamorphism, the Brockman volcanics show excellent preservation of primary volcanological features, including pillow-lavas and pillow-breccias, that suggest a dominantly subaqueous, below-wave-base emplacement environment. The style of eruption products and magma volume constraints suggest the trachyte-dominated volcanics were erupted from a small shield volcanic complex probably in a rift-related basin in a shallow-marine setting. The tectonic setting was intraplate but differs from most Tertiary to recent trachyte volcanic complexes which are largely subaerial, are built on relatively thick continental crust, and show no post-eruptive orogenic history. Brockman-style rare-metal deposits are characterized by preservation of subaqueous volcanics beneath a thick sedimentary sequence, eruption of early incompatible-element enriched products followed by less differentiated magmas, and fine-grained mineralogy influenced by alteration processes. Prospects exist for discovery of analogous deposits, particularly in early Proterozoic mobile belts and Tertiary intraplate shield volcanic provinces.

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Geologie der an Vulkanite gebundenen Seltene-Metalle-Lagerstätte Brockman, Halls Creek Mobile Zone, Nordwest-Australien. I. Vulkanologie, Geochronologie und Petrographie der Brockman-Vulkanite

Zusammenfassung Selten-Metall-Vererzung der Brockman-Lagerstätten (Halls Creek Mobile Zone, NW Australien) sitzt in einer Fluorit-führenden, rhyolitischen vulkanoklastischen Einheit auf, die informell als der Niob-Tuff bezeichnet wird. Es handelt sich hier um ein vulkanoklastisches Tuff-Sediment; dieses ist die unterste Einheit einer Abfolge vor Trachyt bis Rhyolit-Laven, trachyandesitischen Subvulkaniten and vulkanoklastischen Einheiten der Brockman Vulkanite innerhalb der Halls Creek Gruppe, einer mächtigen frühproterozoischen vulkanosedimentdren Abfolge. Prüzisionsdatierungen des Niob Tuffs mit der SHRIMP Ionen-Mikrosonde ergeben ein Eruptionsalter von 1870 +-4 Millionen Jahren. Regionale geochronologische Zusammenhänge zeigen, daß der Niob Tuff etwa 15 Millionen Jahre vor einer größeren Orogenese, die das Gebiet betroffen hat, abgelagert wurde. Trotz Faltung, Bruchtektonik and niedriggradiger Metamorphose zeigen die Brockman-Vulkanite einen hervorragenden Erhaltungszustand primärer vulkanologischer Erscheinungen. Diese urnfassen auch Kissenlaven und KissenBreckzien, die eine vorwiegend subaquatische Ablagerung in ruhigem Wasser erkennen lassen. Die Art der Eruptionsprodukte and das Magmavolumen zeigen, daß die Trachytdominierten Vulkanite von einem kleinen Schildvulkan stammer, wahrscheinlich in einem Becken in einer Rift-Situation im seichten marinen Milieu. Die tektonische Situation war intraplate, aber unterscheidet sich von den meisten tertiären bis rezenten trachytischen Vulkan-Komplexen, die hauptsächlich subaerisch sind, auf einer relativ mächtigen kontinentalen Kruste aufsitzen, and keine post-eruptive orogene Entwicklung zeigen. Seltene-Metalle-Lagerstatten des Brockman-Typs rind durch die Erhaltung subaquatischer-Vulkanite unterhalb einer machtigen sedimentdren Abfolge gekennzeichnet; welters durch frühe Eruptionsprodukte, die an inkompatiblen Elementen angereichert sind, auf die dann weniger differenzierte Magmen folgten, und schließlich durch einen feinkörnigen Mineralbestand, der vor Umwandlungsprozessen betroffen war. Es besteht die Möglichkeit der Entdeckung analoger Lagerstätten, besonders in frühproterozoischen mobilen Gürteln und in tertidren intraplate Schildvulkan Provinzen.

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The oxidation states of cobalt and selected metals in Pacific ferromanganese nodules

A study of the oxidation states of metals in selected Pacific ferromanganese nodules by x-ray photoelectron spectroscopy (XPS) indicates the presence of Co(III), Pb(II), Pb(IV), Fe(III) and Ti(IV). These findings are based on measurements of core electron binding energies and an evaluation of the core electron shake-up satellite features.     

Massless scalar field in Robertson-Walker space-time

Recently, exact spatially-homogeneous solutions have been found for a conformally invariant massless scalar fieldS(t) coupled to a Robertson-Walker geometry. We investigate extending these solutions to inhomogeneous scalar fieldsS(t, x ^l ). For an isotropic scalar fieldS(t, r) we find a solution satisfying three of the five field equations. If we use REDUCE, we show that the remaining equations forceS=S(t).     

Provenance of the Bosnian Flysch

Sandwiched between the Adriatic Carbonate Platform and the Dinaride Ophiolite Zone, the Bosnian Flysch forms a c. 3000 m thick, intensely folded stack of Upper Jurassic to Cretaceous mixed carbonate and siliciclastic sediments in the Dinarides. New petrographic, heavy mineral, zircon U/Pb and fission-track data as well as biostratigraphic evidence allow us to reconstruct the palaeogeology of the source areas of the Bosnian Flysch basin in late Mesozoic times. Middle Jurassic intraoceanic subduction of the Neotethys was shortly followed by exhumation of the overriding oceanic plate. Trench sedimentation was controlled by a dual sediment supply from the sub-ophiolitic high-grade metamorphic soles and from the distal continental margin of the Adriatic plate. Following obduction onto Adria, from the Jurassic–Cretaceous transition onwards a vast clastic wedge (Vranduk Formation) was developed in front of the leading edge, fed by continental basement units of Adria that experienced Early Cretaceous synsedimentary cooling, by the overlying ophiolitic thrust sheets and by redeposited elements of coeval Urgonian facies reefs grown on the thrust wedge complex. Following mid-Cretaceous deformation and thermal overprint of the Vranduk Formation, the depozone migrated further towards SW and received increasing amounts of redeposited carbonate detritus released from the Adriatic Carbonate Platform margin (Ugar Formation). Subordinate siliciclastic source components indicate changing source rocks on the upper plate, with ophiolites becoming subordinate. The zone of the continental basement previously affected by the Late Jurassic–Early Cretaceous thermal imprint has been removed; instead, the basement mostly supplied detritus with a wide range of pre-Jurassic cooling ages. However, a c. 80 Ma, largely synsedimentary cooling event is also recorded by the Ugar Formation, that contrasts the predominantly Early Cretaceous cooling of the Adriatic basement and suggests, at least locally, a fast exhumation.     

Record of Late Pleistocene Glaciation and Deglaciation in the Southern Cascade Range. I. Petrological Evidence from Lacustrine Sediment in Upper Klamath Lake, Southern Oregon

Petrological and textural properties of lacustrine sediments from Upper Klamath Lake, Oregon, reflect changing input volumes of glacial flour and thus reveal a detailed glacial history for the southern Cascade Range between about 37 and 15 ka. Magnetic properties vary as a result of mixing different amounts of the highly magnetic, glacially generated detritus with less magnetic, more weathered detritus derived from unglaciated parts of the large catchment. Evidence that the magnetic properties record glacial flour input is based mainly on the strong correlation between bulk sediment particle size and parameters that measure the magnetite content and magnetic mineral freshness. High magnetization corresponds to relatively fine particle size and lower magnetization to coarser particle size. This relation is not found in the Buck Lake core in a nearby, unglaciated catchment. Angular silt-sized volcanic rock fragments containing unaltered magnetite dominate the magnetic fraction in the late Pleistocene sediments but are absent in younger, low magnetization sediments. The finer grained, highly magnetic sediments contain high proportions of planktic diatoms indicative of cold, oligotrophic limnic conditions. Sediment with lower magnetite content contains populations of diatoms indicative of warmer, eutrophic limnic conditions. During the latter part of oxygen isotope stage 3 (about 37–25 ka), the magnetic properties record millennial-scale variations in glacial-flour content. The input of glacial flour was uniformly high during the Last Glacial Maximum, between about 21 and 16 ka. At about 16 ka, magnetite input, both absolute and relative to hematite, decreased abruptly, reflecting a rapid decline in glacially derived detritus. The decrease in magnetite transport into the lake preceded declines in pollen from both grass and sagebrush. A more gradual decrease in heavy mineral content over this interval records sediment starvation with the growth of marshes at the margins of the lake and dilution of detrital material by biogenic silica and other organic matter.     

The hydrogeochemistry of methane: Evidence from English groundwaters

The presence of methane (CH₄) in groundwater is usually only noticed when it rises to high concentrations; to date rather little is known about its production or natural ‘baseline’ conditions. Evidence from a range of non-polluted groundwater environments in England, including water supply aquifers, aquicludes and thermal waters, reveals that CH₄ is almost always detectable, even in aerobic conditions. Measurements of potable waters from Cretaceous, Jurassic and Triassic carbonate and sandstone aquifers reveal CH₄ concentrations of up to 500 μg/l, but a mean value of < 10 μg/l. However, aquiclude and thermal waters from the Carboniferous and Triassic typically contain in excess of 1500 μg/l. Such high concentrations have so far only been found at redox (Eh) potentials below 0 mV, but in general CH₄ concentration and Eh value are poorly correlated. This suggests a lack of thermodynamic equilibrium, which is confirmed by comparing pe values calculated from the redox couple C(4)/C(− 4) with those derived from Eh. Genesis of CH₄ appears to occur on two timescales: a rapid if low rate of production from labile carbon in anaerobic microsites in the soil, and a much longer, millennium scale of production from more refractory carbon. Methane is rarely measured in groundwater; there is no single ionic determinand which acts universally as a proxy, but a combination of high HCO₃ and low SO₄ concentrations, or the reverse, is an indication that high amounts of CH₄ may be present.     

Sedimentology and palynology of the Calafate Formation (Maastrichtian), Austral Basin, Southern Patagonia, Argentina

The Calafate Formation crops out in south-western Santa Cruz Province, Argentina, and displays a stacking of asymmetrical coarsening–fining-upward cycles. These cycles are interpreted as the product of short-lived transgressive-regressive events in which the coarsening upward part represents sedimentary aggradation with a stable or decreasing sea level. Sedimentological and palynological analyses indicate nearshore marine conditions. Even though the existence of an estuary or incised valley cannot be determined, this is the most probable palaeogeographic model. Based on dinoflagellate cysts, the base of the section is considered to be not older than Maastrichtian. The presence of the oyster Ambigostrea clarae (Ihering) occurring together with the dinoflagellate cyst species Manumiella druggii (Stover) Bujak and Davies and Eisenackia circumtabulata Drugg in the middle part of the section indicates an age no older than late Maastrichtian. According to sedimentological data, deposits representing the Cretaceous–Palaeogene transition would have been eroded, which is confirmed by the presence of Grapnelispora loncochensis Papú. This megaspore is a consistent component of the Maastrichtian assemblages from Patagonia.