Hill stability and distance curves for the general three-body problem

The notion of Hill stability is extended from the circular restricted 3-body problem to the general three-body problem; it is even extended to systems of positive energy and the Hill's curves with their corresponding forbidden zones are generalized.Hill stable systems of negative energy present a hierarchy: they have a close binary that can be neither approached nor disrupted by the third body. This phenomenon becomes particularly clear with the distance curves presentation.The three limiting cases, restricted, planetary and lunar are analysed as well as some real stellar cases.     

Small-scale seismic heterogeneity and mantle structure

George Helffrich discusses the links between seismology and geochemistry in the Bullerwell Lecture 2005, delivered at the annual meeting of the European Union of Geosciences in Vienna.     

Variational stabilization of the ionic charge densities in the electron-gas theory of crystals: Applications to MgO and CaO

The electron-gas theory of crystals is extended to include the effects of many-body forces that arise from both electrostatic and overlap interactions. These effects are incorporated through a self-consistent spherical relaxation of the ionic charge distributions such that the crystal binding energy is minimized. This variational model is used to compute the elastic constants and equations of state of MgO and CaO, and we compare its results to those derived from earlier electron-gas models. In the variational model, the anion charge distributions are markedly more sensitive to the local crystal environment than they are in the PIB or other electron-gas models. We find that for these oxides the variational model gives the best overall agreement with experiment for lattice constants, equations of state, dissociation energies, and elastic moduli.     

Investigation of acidic dissolution of mixed clays between pH 1.0 and −3.0 using Si and Al X-ray absorption near edge structure

Although widely investigated in relation to acid mine drainage systems at pH > 1.0, we know little about the impact of sulfuric acid (H₂SO₄) on the geochemistry and mineralogy of clays at pH < 1.0 (including negative pH values). Thus, laboratory batch experiments were conducted on three mixed clay samples with different mass ratios of phyllosilicates (smectite, illite, and kaolinite) to investigate the impact of H₂SO₄ from pH 1.0 to −3.0 for exposure periods of 14, 90, 180, and 365 days. Si and Al K- and L_2,3-edge X-ray absorption near edge structure (XANES) spectroscopy were employed on these samples to determine the chemical and structural changes that occur during acidic dissolution of phyllosilicates that cannot be distinguished using X-ray diffraction analyses. A series of silicate, phyllosilicate, and Al-bearing standard compounds were also studied to provide an explanation for the observed changes in the clay samples. The Si XANES results indicated the preferential dissolution of the phyllosilicates (pH ? 1.0, t ? 14 d), the persistence of quartz even at pH ? −3.0 and t ? 365 d, and the formation of an amorphous silica-like phase that was confined to the surface layer of the altered clay samples at pH ? 0.0 and t ? 90 d). Al XANES results demonstrated dissolution of Al-octahedral layers (pH ? 1.0, t ? 14 d), the persistence of four-fold relative to six-fold coordinated Al, and the precipitation of an Al-SO₄-rich phase (pH ? −1.0, t ? 90 d). An existing conceptual model of phyllosilicate dissolution under extremely acidic conditions was modified to include the results of this study.     

An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system

A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi‐analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time‐domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic stochastic estimation of physical variables

A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects.     

Glaciation and ~ 770 Ma Ediacara (?) Fossils from the Lesser Karatau Microcontinent,Kazakhstan

The Cambrian explosion, c. 530–515 Ma heralded the arrival of a diverse assembly of multicellular life including the first hard-shelled organisms. Fossils found in Cambrian strata represent the ancestors of most modern animal phyla. In contrast to the apparent explosiveness seen in the Cambrian fossil record, studies of molecular biology hint that the diversification observed in Cambrian strata was rooted in ancestry extending back into the Ediacaran (635–542 Ma). Fossil evidence for this mostly cryptic phase of evolution is derived from the soft-bodied fossils of the Ediacaran biota found throughout the world and bilaterian embryos found in the Doushantuo lagerstätte in South China. The first appearance of Ediacara fauna is thought to have followed the last of the ~ 750–635 Ma Neoproterozoic glacial episodes by 20–30 million years. In this paper, we present evidence for the oldest discovery of the ‘Ediacara’ discoidal fossils Nimbia occlusa and Aspidella terranovica (?) that predate the early Cryogenian glaciations by more than fifty million years. There is considerable disagreement over the significance of discoidal Ediacaran fossils, but our findings may support earlier suggestions that metazoan life has roots extending deeper into the Proterozoic Eon. We also confirm the presence of a Late Cryogenian (e.g. “Marinoan”) glaciation on the Lesser Karatau microcontinent including dropstones and striated clasts within the glacial strata.