Convergence of Liapunov Series for Maclaurin Ellipsoids

According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q ₀ may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q ₀ for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q ₀ = 0.337 for Maclaurin ellipsoids.     

On the sublimation of ice particles on the surface of Mars; with applications to the 2007/8 Phoenix Scout mission

Experimental studies related to the sublimation of ice, in bulk or as small particles, alone or mixed with dust similar to that expected on the surface of Mars, are reported. The experiments, a cloud physics particle sublimation model, and a convection model presented by Ingersoll, all indicate a strong dependence of sublimation rate on temperature, and this appears to be the dominant factor, assuming that the relative humidity of the air is fairly low. In addition the rate of loss of water vapour appears to depend primarily on exposed surface area and less on particle size and the total mass of the sample, or the mass of ice in the sample. The 2007/8 Phoenix Scout mission plans to obtain and analyse samples of sub-surface ice from about 70° N on Mars. A concern is that these samples, in the form of ice chips of size about 1 mm diameter, could be prone to sublimation when exposed for prolonged periods (many hours) to a relatively warm and dry atmosphere. Our laboratory simulations confirm that this could be a problem if particles are simply left lying on the surface, but also indicate that samples kept suitably cold and collected together in confined piles will survive long enough for the collection and delivery (to the analysis instruments) procedure to be completed.     

Onset of secular chaos in planetary systems: period doubling and strange attractors

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula.     

Rodingites from the Veria-Naousa ophiolite (Greece): Mineralogical evolution,metasomatism and petrogenetic processes

In the Veria-Naousa ophiolitic complex (north Greece), rodingite appears mainly in the form of cross cutting dykes within serpentinised peridotites. It is distinguished into three types, based upon the provenance of its protoliths, textural characteristics, mineralogical assemblages and geochemical affinities. Type I rodigites were derived from boninitic diabasic protoliths and their mineralogical assemblage include garnet + clinopyroxene + chlorite. Type II rodingites were formed at the expense of gabbroic precursors, comprising clinopyroxene + garnet + vesuvianite ± quartz, whereas Type III rodingites replaced diabasic tholeiitic protoliths comprising of garnets + vesuvianite + clinopyroxene + chlorite. Rodingitisation resulted in desilification, decrease of alkalies, Al, Fe, Mg and increase in Ca contents. In Type I rodingites the MREE (middle rare earth elements) and HREE (heavy rare earth elements) were slightly reduced. Type II rodingites experienced LREE (light rare earth elements) depletions, whereas MREE and HREE remained fairly stable. Restricted mobility of REE in Type III rodingites is assigned to shallow-level rodingitisation under decreasing pH.Rodingitisation occured in two distinct stages at fore-arc settings. The first stage occured under mildly oxidising conditions and enhanced CO₂/H₂O ratios. This stage affected the protoliths of all rodingite types. The second rodingitisation stage occured under more oxidising conditions and lower CO₂/H₂O ratios, which corresponds to the exhumation stage of the serpentinite-rodingite formations. Types II and III rodingites were subjected to further rodingitisation under the increasing influence of slab-derived hydrous phases at shallower depths, leading to the formation of late-stage andradite and vesuvianite. All stages of rodingitisation are estimated to have occurred under relatively moderate temperatures and pressure (~300 to 450 °C; ~2–6 kbar respectively).     

Tappania-bearing association of the Siberian platform: Biodiversity, stratigraphic position and geochronological constraints

A new fossil microbiota yielding eukaryotic Tappania is described from the Mesoproterozoic Kamo Group of the Central Angara Basin, Siberian Craton. The assemblage also includes Valeria, Satka, Lophosphaeridium, Pulvinosphaeridium, Miroedichia, Osculosphaera, Tasmanites, Obruchevella, Glomovertella, as well as branching and anastomosing filamentous microfossils of putative fungal affinities and peculiar short trichomes, that together substantially increase the biodiversity of the Tappania Association. Stratigraphic position and geochronological constraints indicate a relatively young Late Mesoproterozoic age of the Tappania-bearing sediments. There appears to be a continuity between the Tappania Association and the Neoproterozoic microbiota, the latter being firmly rooted in the Late Mesoproterozoic.     

High-Latitude Geomagnetic Disturbances and Field Aligned Currents in the Recovery Phase of the Large Magnetic Storm on June 21–26, 2015

Geomagnetism and Aeronomy - The features of the geomagnetic effect of the approach of an interplanetary magnetic cloud to the Earth’s magnetosphere during the recovery phase of a strong...     

Hydrological modelling for assessing spatio-temporal groundwater recharge variations in the water-stressed Amathole Water Supply System,Eastern Cape,South Africa

To increase the resilience of regional water supply systems in South Africa in the face of anticipated climatic changes and a constant increase in water demand, water supply sources require diversification. Many water-stressed metropolitan regions in South Africa depend largely on surface water to cover their water demand. While climatic and river discharge data is widely available in these regions, information on groundwater resources – which could support supply source diversification – is scarce. Groundwater recharge is a key parameter that is used to estimate groundwater amounts that can be sustainably exploited at a sub-watershed level. Therefore, the objective of this study was to develop a reliable hydrological modelling routine that enables the assessment of regional spatio-temporal variations of groundwater recharge to discern the most promising areas for groundwater development. Accordingly, we present a semi-distributed hydrological modelling approach that incorporates water balance routines coupled with baseflow modelling techniques to yield spatio-temporal variations of groundwater recharge on a regional level. The approach is demonstrated for the actively managed catchment areas of the Amathole Water Supply System situated in a semi-arid part of the Eastern Cape of South Africa. In the investigated study area, annual groundwater recharge exhibits a high spatio-temporal heterogeneity and is estimated to vary between ~0.5% and 8% of annual rainfall. Despite some uncertainties induced by limited data availability, calibration and validation of the model were found to be satisfactory and yielded model results similar to (point) data of annual groundwater recharge reported in earlier studies. Our approach is therefore found to derive crucial information for efficiently targeting more detailed groundwater exploration studies and could work as a blueprint for orientating groundwater potential exploration in similar environments.     

On the Distance Function Between Two Keplerian Elliptic Orbits

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

Advection of passive scalars induced by a bay-trapped nonstationary vortex

A simple model of fluid particle advection induced by the interaction of a point vortex and incident plane flow occurring near a curved boundary is analyzed. The use of the curved boundary in this case is aimed at mimicking the geometry of an isolated bay of a circular shape. An introduction of such a boundary to the model results in the appearance of retention zones, where the vortex can be permanently trapped being either stationary or periodically oscillating. When stationary, it induces a steady velocity field that in turn ensures regular advection of nearby fluid particles. When the vortex oscillates periodically, the induced velocity field turns unsteady leading to the manifestation of chaotic advection of fluid particles. We show that the size of the fluid region engaged into chaotic advection increases almost monotonically with the increased magnitude of the vortex oscillations provided the magnitude remains relatively small. The monotonicity is accounted for the fact that the frequency of the vortex oscillations incommensurable with the proper frequency of fluid particle rotations in the steady state. Another point of interest is that it is demonstrated that bounded regions, in which the vortex may be trapped, can appear even at a significant distance from the bay. Making use of a Lagrangian indicator, examples of fluid particle advection induced by the periodic motion of the vortex inside the bay are adduced.