Libration effects for retrograde satellites in the restricted three-body problem

Numerical explorations of the restricted problem have shown that for stable large nonperiodic retrograde satellite orbits, the motion can be decomposed into a fast reference motion and a slow libration aroundB ₂ We study here this libration in the circular plane Hill's case, for which the reference motion is elliptic. We establish the equations of motion for the coordinates of the centre of this ellipse. We find two integrals of motion: the first is the semi-major axis of the ellipse; the second is essentially Jacobi's integral, translated into the new coordinates. We give a formula for the period of the libration and we find its limiting value for small libration amplitudes. A numerical verification gives very good agreement for all these results.     

On the structure of Saturn's rings and the ‘real’ rotational period for the planet

An analysis of the Lowell Observatory photographic plates of Saturn gave the following results: (1) ring A and B show peculiar brightness distributions around the planet, from which we conclude that both are composed of particles in synchronous rotation. (2) The leading side of the particles in ring A is brighter than the trailing side by about 4%, which may indicate an interaction between such particles and the interplanetary medium. (3) Scans of the rings across the major axis show a small (～0.3″) region of enhanced brightness, from which we derive a value ofT _s =10^h13 _. ^m 8±5 _. ^m 4 for the actual planetary rotational period of Saturn. (4) In order to explain the synchronous rotation, the particles in ring A have to be at least 42 m in diameter.     

Layered mantle structure beneath the western Guyana Shield, Venezuela: Evidence from diamonds and xenocrysts in Guaniamo kimberlites

Mantle xenoliths and xenocrysts from Guaniamo, Venezuela kimberlites record equilibration conditions corresponding to a limited range of sampling in the lithosphere (100-150 km). Within this small range, however, compositions vary considerably, but regularly, defining a strongly layered mantle sequence. Major and trace element compositions suggest the following lithologic sequence: highly depleted lherzolite from 100 to 115 km, mixed ultra-depleted harzburgite and lherzolite from 115 to 120 km, relatively fertile lherzolite from 120 to 135 km, and mixed depleted harzburgite and relatively fertile lherzolite from 135 to 150 km. Based on comparison with well-documented mantle peridotites and xenocrysts from elsewhere, we conclude that the Meso-proterozoic Cuchivero Province (host to the Guaniamo kimberlites) is underlain by depleted and ultra-depleted shallow Archean mantle that was underplated, and uplifted, by Proterozoic subduction, perhaps more than once. These Proterozoic subduction events introduced less-depleted oceanic lithosphere beneath the Archean section, which remains there and is the source of the abundant Guaniamo eclogite-suite diamonds that have ocean-floor geochemical signatures. Although diamond-indicative low-Ca Cr-pyrope garnets are abundant, they are derived primarily from the shallow depleted layer within the field of graphite stability, and the rare peridotite-suite diamonds are either metastably preserved at these shallow depths, or were derived from the small amount of depleted lithosphere sampled by these kimberlites that remains within the diamond stability field (the mixture of Archean and Proterozoic mantle in the depth range 135-150 km).     

Source(s) and cycling of the nonhydrolyzable organic fraction of oceanic particles

A major fraction of particulate organic carbon (POC) in the deep ocean remains molecularly uncharacterized. In an effort to determine the chemical characteristics and source(s) of sinking POC, we studied a nonhydrolyzable fraction of sinking POC using ¹³C NMR (nuclear magnetic resonance) spectroscopy and analytical pyrolysis. ¹³C NMR spectra and products from analytical pyrolysis of the nonhydrolyzable fraction exhibit a strongly aliphatic character that is distinct from that of bulk POC. The aliphatic nature of this fraction is consistent with its low stable carbon isotope values. We hypothesize that the nonhydrolyzable fraction derives to a significant extent from a refractory component of organisms that selectively accumulates, resulting in its manifestation as a major part of POC sinking to the deep ocean and in underlying sediments.     

Review: Microbial biocenoses in pristine aquifers and an assessment of investigative methods

The current knowledge of microbial biocenoses (communities) in pristine aquifers is presented in a review, which also discusses their relevance for questions of groundwater protection. Aquifers are heterogeneous on all scales and structured in a variety of habitats. The void spaces in many aquifers are small. The biocenoses are thus predominantly composed of microorganisms and, often, microinvertebrates. Larger voids and macroorganisms occur in karst cavities. Due to the absence of light, the biocenoses depend on chemical energy resources, which are, however, scarce in non-contaminated groundwater. The microorganisms thus show small cell sizes, low population densities and reduced activity; they developed specific strategies to survive oligotrophic conditions. The review also discusses the impact of contamination on the biocenoses, and the potential use of the biocenoses or specific organisms as indicators for groundwater quality, and the limits of this approach. Bacteria are either planktonic or attached to aquifer material, which requires both fluid and solid phase sampling. Most groundwater bacteria are viable but non-culturable. Consequently, cultivation techniques give an incomplete picture of the biocenoses, while methods from molecular microbiology provide genetic fingerprints of the entire community. Different analytical methods are available to count microorganisms, identify species, characterise microbial diversity, and measure activity.     

Study of geothermal water intrusion due to groundwater exploitation in the Puebla Valley aquifer system, Mexico

Significant intrusion of geothermal water into fresh groundwater takes place in the Puebla Valley aquifer system, Mexico. The decline in the potentiometric surface due to the overexploitation of the groundwater induces this intrusion. This hydrological system comprises three aquifers located in Plio-Quaternary volcanic sediments and Mesozoic calcareous rocks. The hydraulic balance of the aquifer shows that the annual output exceeds the natural inputs by 12 million m³. Between 1973 and 2002, a drop in the potentiometric surface, with an 80 m cone of depression, was identified in a 5-km-wide area located southwest of the city of Puebla. Chemical analyses performed on water samples since 1990 have shown an increase in total dissolved solids (TDS) of more than 500 mg/L, coinciding with the region showing a cone of depression in the potentiometric surface. A three-dimensional flow and transport model, based on the hydrogeological and geophysical studies, was computed by using the MODFLOW and MT3D software. This model reproduces the evolution of the aquifer system during the last 30 years and predicts for 2010 an additional drawdown in the potentiometric surface of 15 m, and an increase in the geothermal water intrusion.     

Monte Carlo simulation of mixing in Ca3Fe2Ge3O12–Ca4Ge4O12 garnets and implications for the thermodynamic stability of pyrope–majorite solid solution

Static lattice energy calculations, based on empirical pair potentials, were performed for a large set of structures differing in the arrangement of octahedral cations within the garnet 2 × 2 × 2 supercell. The compositions of these structures varied between Ca₃Fe₂Ge₃O₁₂ and Ca₄Ge₄O₁₂. The energies were cluster expanded using pair and quaternary terms. The derived ordering constants were used to constrain Monte Carlo simulations of temperature-dependent mixing properties in the ranges of 1,073–3,673 K and 0–10 GPa. The free energies of mixing were calculated using the method of thermodynamic integration. The calculations predict a wide miscibility gap between Fe-rich (cubic) and Fe-pure (tetragonal) garnets consistent with recent experimental observations of Iezzi et al. (Phys Chem Miner 32:197–207, 2005). It is shown that the miscibility gap arises due to a very strong cation ordering at the Fe-pure composition, driven by the charge difference between Ca²⁺ and Ge⁴⁺ cations. The structural and thermodynamic analogies between Ca–Ge and Mg–Si systems suggest that a similar miscibility gap should exist between pyrope and Mg–Si-majorite.     

Catastrophic debris flows near Machu Picchu village (Aguas Calientes), Peru

Slope movements together with intensive river erosion and the following accumulation are the leading processes in the landscape evolution in the area of Machu Picchu village (former Aguas Calientes), which is located close to the Machu Picchu Sanctuary. Debris flows affect not only the bottoms of valleys or canyons, but also debris fans at the termini of the drainage basins, which are heavily inhabited at some places. The most recent event in the Machu Picchu village occurred in April 2004, but several others were documented in a broader area in the last 50 years. The field inspections at Machu Picchu (May and September 2004; June and September 2005) together with oral testimony revealed the nature and behavior of the debris flow. Machu Picchu village can be assessed as a zone with high landslide risk in relation to its urban development. Despite that, the village recorded a rapid growth (threefold population increase) without urban control within the past two decades. Precipitation, which is the main triggering factor of the debris flows, and natural hazard management of the Machu Picchu village are discussed in this paper.     

The Spačice eclogite: constraints on the P–T–t history of the Gföhl granulite terrane, Moldanubian Zone, Bohemian Massif

Summary In the Kutná Hora Complex, the Běstvina Formation, which is similar to Gf?hl granulite, contains eclogite that has escaped widespread retrograde recrystallization. The eclogite assemblage, garnet + omphacite + quartz + rutile ± plagioclase, yields an estimate for peak metamorphic conditions of 18–20 kbar and 835–935 °C, which is comparable to that determined from felsic granulite, 14–20 kbar and 900–1000 °C. Garnet in eclogite exhibits both prograde and retrograde compositional zoning, from which constraints on thermal history of the Gf?hl terrane can be derived by diffusion modelling. At 900 °C, a garnet grain of 800–1000 μm radius would homogenize in 7.5–11.7 million years, but the existence of compositional gradients on a length scale of 100–200 μm suggests that the duration of peak metamorphism may have been limited to ∼500,000 years. Diffusion modelling of retrograde zoning in garnet yields a cooling rate of 150–100 °C/m.y. for a radius of 800–1000 μm and initial temperature of 900 °C. The relatively brief duration of high-pressure/high-temperature metamorphism and rapid cooling and exhumation of the Gf?hl terrane may be a consequence of lithospheric delamination during Early Carboniferous collision of Bohemia (Teplá-Barrandia) and Moldanubia (Franke, 2000).