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.     

New models of interstellar gas–grain chemistry – III. Solid CO2

Solid CO₂ is observed to be an abundant interstellar ice component towards both quiescent clouds and active star-forming regions. Our recent models of gas–grain chemistry, appropriate for quiescent regions, severely underproduce solid CO₂ at the single assumed gas density and temperature. In this paper, we investigate the sensitivity of our model results to changes in these parameters. In addition, we examine how the nature of the grain surface affects the results and also consider the role of the key surface reaction between O and CO. We conclude that the observed high abundance of solid CO₂ can be reproduced at reasonable temperatures and densities by models with diffusive surface chemistry, provided that the diffusion of heavy species such as O occurs efficiently.     

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.     

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).     

Burying receivers for improved time‐lapse seismic repeatability: CO2CRC Otway field experiment

4D seismic is widely used to remotely monitor fluid movement in subsurface reservoirs. This technique is especially effective offshore where high survey repeatability can be achieved. It comes as no surprise that the first 4D seismic that successfully monitored the CO₂ sequestration process was recorded offshore in the Sleipner field, North Sea. In the case of land projects, poor repeatability of the land seismic data due to low S/N ratio often obscures the time‐lapse seismic signal. Hence for a successful on shore monitoring program improving seismic repeatability is essential. Stage 2 of the CO2CRC Otway project involves an injection of a small amount (around 15,000 tonnes) of CO₂/CH₄ gas mixture into a saline aquifer at a depth of approximately 1.5 km. Previous studies at this site showed that seismic repeatability is relatively low due to variations in weather conditions, near surface geology and farming activities. In order to improve time‐lapse seismic monitoring capabilities, a permanent receiver array can be utilised to improve signal to noise ratio and hence repeatability. A small‐scale trial of such an array was conducted at the Otway site in June 2012. A set of 25 geophones was installed in 3 m deep boreholes in parallel to the same number of surface geophones. In addition, four geophones were placed into boreholes of 1–12 m depth. In order to assess the gain in the signal‐to‐noise ratio and repeatability, both active and passive seismic surveys were carried out. The surveys were conducted in relatively poor weather conditions, with rain, strong wind and thunderstorms. With such an amplified background noise level, we found that the noise level for buried geophones is on average 20 dB lower compared to the surface geophones. The levels of repeatability for borehole geophones estimated around direct wave, reflected wave and ground roll are twice as high as for the surface geophones. Both borehole and surface geophones produce the best repeatability in the 30–90 Hz frequency range. The influence of burying depth on S/N ratio and repeatability shows that significant improvement in repeatability can be reached at a depth of 3 m. The level of repeatability remains relatively constant between 3 and 12 m depths.     

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.     

The shedding of mesoscale anticyclonic eddies from the Alaskan Stream and westward transport of warm water

The south-flowing waters of the Kamchatka and Oyashio Currents and west-flowing waters of the Alaskan Stream are key components of the western sub-Arctic Pacific circulation. We use CTD data, Argo buoys, WOCE surface drifters, and satellite-derived sea-level observations to investigate the structure and interannual changes in this system that arise from interactions among anticyclonic eddies and the mean flow. Variability in the temperature of the upstream Oyashio and Kamchatka Currents is evident by warming in mesothermal layer in 1994–2005 compared to 1990–1991. A major fraction of the water in these currents is derived directly from the Alaskan Stream. The stream also sheds large anticyclonic (Aleutian) eddies, averaging approximately 300 km in diameter with a volume transport significant in comparison with that of the Kamchatka Current itself. These eddies enclose pools of relatively warm and saline water whose temperature is typically 4 °C warmer and salinity is 0.4 greater than that of cold-core Kamchatka eddies in the same density range. Aleutian eddies drift at approximately 1.2 km d⁻¹ and retain their distinctive warm and salty characteristics for at least 2 years. Selected westward pathways during 1990–2004 are identified. If the shorter northern route is followed, Aleutian eddies remain close to the stream and persist sufficiently long to carry warm and saline water directly to the Kamchatka Current. This was observed during 1994–1997 with substantial warming of the waters in the Kamchatka Current and upstream Oyashio. If the eddies take a more southern route they detach from the stream but can still contribute significant quantities of warm and saline water to the upstream Oyashio, as in 2004–2005. However, the eddies following this southern route may dissipate before reaching the western boundary current region.     

Bonded-particle model-based simulation of artificial rock subjected to cyclic loading

A nonlinear parallel-bonded stress corrosion (NPSC) model is proposed to simulate the fatigue characteristics of artificial rock (concrete) during cyclic loading. Numerical simulations of fatigue tests replicate the main mechanical features of concrete specimens subjected to cyclic loading observed in the laboratory. A nonlinear reduction speed of the bond diameter between two bonded particles represents the damage rate induced by the fatigue load. The damage rate is proportional to the maximum cyclic load level when the minimum cyclic load level is fixed. Compared with laboratory data, a logarithmic function of bond diameter in the NPSC model resulted in the best fit to simulate the fatigue behaviour of concrete. The simulation includes acoustic emission (AE) monitoring during fatigue tests. The axial strain of the assembly is governed by the evolution of bond breakages. The sum of released bond strain energy is documented as value proportional to cumulative AE energy. The simulation results show very similar evolution compared with laboratory data, which verifies the effectiveness of AE energy simulation.