A transformation of the two-body problem

A transformation of the differential equations of motion of the two-body problem in the spherical coordinates to oscillator form is derived. It is shown that the independent variable transformation dt/ds=r² is a transformation which makes the oscillator form possible.     

Does sediment grain size affect diatom grazing by harpacticoid copepods?

Estuarine soft sediments support a diverse group of eukaryotic and prokaryotic organisms though the role of the sediment per se for the functioning of these organisms remains largely unknown. The present study aimed to test the effect of sediment grain size on the grazing activities of harpacticoid copepods. In controlled experiments, two common intertidal harpacticoid species (Paramphiascella fulvofasciata and Nitokra spinipes) were each offered a mix of two benthic diatom species (Navicula phyllepta and Seminavis robusta) in different sedimentary conditions. Several microcosms were created using a variety of sediment types, including fine silt (<63 microm), coarser grained sands (125-250, 250-450, 100-300 microm), artificial 'sediments' of glass beads (250-500, 2000 microm) and even the absence of sediment was tested. The diatoms were enriched in the stable carbon (13)C to facilitate tracing in the harpacticoids. Both copepod species were able to graze on the diatoms with highest uptake when sediment was absent. In contrast, both harpacticoid species showed no uptake in silty conditions. In general, grazing was favoured when mean sediment grain size increased. The strong negative effect of fine grains on the grazer's efficiency can be explained by the resulting differences in the structure (and accessibility) of the diatom biofilm on the one hand and the mobility of the grazer on the other hand. In view of the subtle equilibrium between primary producers and grazers, these results might have important implications for the effect of siltation of tidal flats due to, e.g., human activities.     

Numerical Stabilization of Orbital Motion

Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders.     

Late Carboniferous porphyry copper mineralization at La Voluntad,Neuquén,Argentina: Constraints from Re–Os molybdenite dating

The La Voluntad porphyry Cu–Mo deposit in Neuquén, Argentina, is one of several poorly known porphyry-type deposits of Paleozoic to Early Jurassic age in the central and southern Andes. Mineralization at La Voluntad is related to a tonalite porphyry from the Chachil Plutonic Complex that intruded metasedimentary units of the Piedra Santa Complex. Five new Re–Os molybdenite ages from four samples representing three different vein types (i.e., quartz–molybdenite, quartz–sericite–molybdenite and quartz–sericite–molybdenite ± chalcopyrite–pyrite) are identical within error and were formed between ~312 to ~316 Ma. Rhenium and Os concentrations range between 34 to 183 ppm and 112 to 599 ppb, respectively. The new Re–Os ages indicate that the main mineralization event at La Voluntad, associated to sericitic alteration, was emplaced during a time span of 1.7 ± 3.2 Ma and that the deposit is Carboniferous in age, not Permian as previously thought. La Voluntad is the oldest porphyry copper deposit so far recognized in the Andes and indicates the presence of an active magmatic arc, with associated porphyry style mineralization, at the proto-Pacific margin of Gondwana during the Early Pennsylvanian.     

Advances in our understanding of the gem corundum deposits of the West Pacific continental margins intraplate basaltic fields

Recent discoveries over the last decade of new gemfields, exploitation of new and existing deposits, and application of relatively new techniques have greatly increased our knowledge of the basalt-derived gem sapphire–ruby–zircon deposits. In this paper we focus on the Late Mesozoic to Cenozoic intraplate basaltic fields of the West Pacific continental margins. We review advances made in understanding the genesis of these deposits, based on the application of newer techniques. We also critically review existing data on the gem corundum deposits, in order to further refine a model for their origin.In some of the intraplate basaltic fields, corundum-bearing xenoliths have been found showing a range of PT formation conditions from 790 °C at 0.85 GPa to as much as 1100 to 1200 °C at 1.0 to 2.5 GPa. Although most magmatic sapphires contain syngenetic inclusions of columbite-group phases, zircon, spinel and rutile, some contain additional nepheline and K-feldspar, suggesting crystallization from more undersaturated alkaline magma while the Weldborough field of NE Tasmania also contains molybdenite and beryl, suggesting at least some interaction with more fractionated ‘granitic-type’ magmas. There is a large range in PT conditions calculated for the metamorphic rubies (from 780 to 940 °C, through 800 to 1150 °C up to 1000 to 1300 °C). Fluid/melt inclusion studies on magmatic corundums generally suggest that they formed in a CO₂-rich environment from a ‘syenitic’ melt under a range of T conditions from 720 to 880 °C up to 1000 to 1200 °C. Oxygen isotope studies reveal that typical magmatic corundums have values of + 4.4 to 6.9‰, whereas metamorphic corundums from the same basaltic host have lower values of + 1.3 to 4.2‰.Geochronological studies have shown that some fields produced a simple eruptive and zircon/corundum crystallization event while others had multiple eruptive events but only one or two zircon crystallization events. For a few fields, some corundums/zircons crystallized in storage regions and then remained relatively inert for periods of 200 to 400 Ma without significant change before transport to the surface in the Cenozoic. Tectonic studies of the Australian region suggest that many of the corundums crystallized from magmas related to episodic basaltic volcanism in a tectonic regime of extension, associated with the opening of the Tasman and Coral Seas. For the Asian region, the magmatic–polygenetic corundums within the basaltic fields largely crystallized in a tectonic regime of distributed E–W extension, whereas the metamorphic-metasomatic corundums crystallised in a transpressional regime associated with the collision of the Indian Plate with the Eurasian Plate (e.g., [Garnier, V., Giuliani, G., Maluski, H., Ohnenstetter, D., Deloule, E., 2003. Ar–Ar and U–Pb ages of marble-hosted ruby deposits from Central and South-east Asia. Geophysical Research Abstracts 5, 03751; Garnier, V., Giuliani, G., Ohnenstetter, D., and Schwarz, D., 2004. Les gisements de corindon: classification et genese. Les placers a corindon gemme. Le Regne Mineral 55, 7-47; Garnier, V., Ohnenstetter, D., Giuliani, G., Maluski, H., Deloule, E., Phan Trong, T., Pham Van, L., Hoang Quang, V., 2005a. Age and significance of ruby-bearing marble from the Red River Shear Zone, Northern Vietnam. Canadian Mineralogist 43, 1315–1329]).     

Defect properties of albite

Knowledge of the defect properties of Lunar and Mercurian minerals has recently become important, with the advent of models which attempt to explain the formation of the thin exosphere of these celestial bodies. Here, we have calculated the formation energies of sodium and oxygen vacancies in the mineral albite (NaAlSi₃O₈), as well as the Schottky defect energy for the removal of a Na₂O unit. We have employed both the supercell and Mott–Littleton approaches, using Kohn–Sham density functional theory and classical interatomic potential methods. As well as reporting the defect energies and structures, we comment upon the relative merits of the methods used.     

Pole-to-pole moisture conditions for the IGY

Summary A study of the mean atmospheric humidity conditions on a planetary scale during the IGY covering the calendar year 1958 is presented. The fields of mean precipitable water content and of the zonal and meridional transports of water vapor are analyzed for the entire globe. Zonally averaged values of the various quantities at several levels are presented in tabular form and compared whenever possible with previous results or indirectly are analyzed on the basis of information obtained from different sources. The structure of these fields is studied and the corresponding implications for the general circulations of the atmosphere are discussed. Finally the zonal water balance for all the globe is discussed and its implications analyzed.     

Galactic dynamics in the light of meteorological theory

Summary Equations for the motions in a galaxy which is controlled by gravitational forces and inertial effects are formulated. It is found that for the motions relative to the rotating system formulae analogous, and of similar form, to the geostrophic wind equations may be written. From these formulae and from the distribution of the relative gravitational potential in the disc of the galaxy, it is found that a spiral tendency in the mass distribution carries the implication of an inward flux of angular momentum by advective processes. This is to be compared with an outward flux through gravitational torques obtained in previous studies in which the writer participated.     

A sidelight on long range forecasting

Summary A gradually cumulative error due to the use of the hydrostatic approximation is examined through consideration of a simple mathematical model taken from the classical theory of gravity waves. Two cases are chosen which differ solely in the circumstance that in one the hydrostatic assumption is made while in the other it is not. A large divergence of the results present in the later stages is then to be referred to the neglect of terms contained in the exact equation of motion for the vertical direction in one of the solutions. The inference is drawn that comparable phenomena might arise in the integration of the atmospheric equations over long time periods.     

On the nonlinear uncoupled roll and pitch of submerged vehicles

This paper presents an exact solution of the problem of free nonlinear rolling or pitching motion of a submerged vehicle. The nondimensional frequency-amplitude relationship of free uncoupled roll or pitch is universal, i.e. the single curve describes the behavior of any vehicle. This relationship is softening, i.e. the decreasing frequencies correspond to larger amplitudes of roll or pitch. The amplitudes of vibrations in the region of frequencies corresponding to the resonance are very sensitive to small variations of the frequency. These conclusions, i.e. the softening nonlinearity and the high sensitivity of the amplitudes to small variations of the vibration frequency are valid also for the problem of forced nonlinear roll or pitch motion of submerged vehicles.