The collision singularity in a perturbed two-body problem

It is shown that, in the neighborhood of a collision singularity, the motion in a perturbed two-body problem \(\ddot r = - \mu r^{ - 3} r + P\) , whereP remains bounded, has the same basic properties as the motion in the neighborhood of a collision in the unperturbed two-body problemP=0.     

Evidence for focused hot fluid flow within the Britannia Field, offshore Scotland, UK

Fluid inclusion and scanning electron microscope‐cathodoluminescence evidence indicates focused hot, saline, diagenetic fluid flow within the Eastern Flank of the Britannia Field, offshore Scotland, UK. The fluid was sourced from the Andrew Salt Dome, 10 km to the east. The fluids, which promoted quartz cementation of the upper zones within the field, were up to ～30°C hotter and had salinities up to ～10 wt% NaCl equivalent higher than fluids from lower in the reservoir section. During diagenesis hot saline fluids migrated westwards as part of a radiating ‘diagenetic front’ from the Andrew Salt Dome. Structural dip associated with the Eastern Flank of the Fladen Ground Spur impeded the westward movement of the diagenetic fluid. The quartz cements from the upper and lower reservoir zones can be distinguished by morphology. In the upper zones the quartz cements have well‐developed macro‐crystalline zoning and heterogeneous luminescence across the grain. In the lower zones, the cements are much less developed, unzoned and very weakly luminescent. The diagenetic fluids were primarily focused into Zone 45 within the upper reservoir. Furthermore, within the Main Platform Area the most prolific producing zone is Zone 45, indicating the importance of this interval as a permeable flow unit during both diagenetic and production timescales. Within the Eastern Flank, the quartz overgrowths have a major impact on reservoir permeability and thus well productivity. The overgrowths are most extensive in the originally clean sandstones with low clay content. Clay in optimum volumes (5–10%) can inhibit nucleation of the damaging quartz overgrowths without having a detrimental effect on pore connectivity. These observations provide a predictive concept for use in the search for relative reservoir sweetspots within the degraded Eastern Flank.     

Trace-element composition and zoning in clinopyroxene- and amphibole-group minerals: Implications for element partitioning and evolution of carbonatites

The present work is a first comprehensive study of the trace-element composition and zoning in clinopyroxene- and amphibole-group minerals from carbonatites, incorporating samples from 14 localities worldwide (Afrikanda, Aley, Alnö, Blue River, Eden Lake, Huayangchuan, Murun, Oka, Ozernaya Varaka, Ozernyi, Paint Lake, Pinghe, Prairie Lake, Turiy Mys). The new electron-microprobe data presented here significantly extend the known compositional range of clinopyroxenes and amphiboles from carbonatites. These data confirm that calcic and sodic clinopyroxenes from carbonatites are not separated by a compositional gap, instead forming an arcuate trend from nearly pure diopside through intermediate aegirine–augite compositions confined to a limited range of CaFeSi₂O₆ contents (15–45 mol%) to aegirine with < 25 mol% of CaMgSi₂O₆ and a negligible proportion of CaFeSi₂O₆. A large set of LA-ICPMS data shows that the clinopyroxenes of different composition are characterized by relatively low levels of Cr, Co and Ni (≤ 40 ppm) and manifold variations in the concentration of trivalent lithophile and some incompatible elements (1–150 ppm Sc, 26–6870 ppm V, 5–550 ppm Sr, 90–2360 ppm Zr, and nil to 150 ppm REE), recorded in some cases within a single crystal. The relative contribution of clinopyroxenes to the whole-rock Rb, Nb, Ta, Th and U budget is negligible. The major-element compositional range of amphiboles spans from alkali- and Al-poor members (tremolite) to Na–Al-rich Mg- or, less commonly, Fe-dominant members (magnesiohastingsite, hastingsite and pargasite), to calcic–sodic, sodic and potassic–sodic compositions intermediate between magnesio-ferrikatophorite, richterite, magnesioriebeckite, ferri-nyböite and (potassic-)magnesio-arfvedsonite. In comparison with the clinopyroxenes, the amphiboles contain similar levels of tetravalent high-field-strength elements (Ti, Zr and Hf) and compatible transition elements (Cr, Co and Ni), but are capable of incorporating much higher concentrations of Sc and incompatible elements (up to 500 ppm Sc, 43 ppm Rb, 1470 ppm Sr, 1230 ppm Ba, 80 ppm Pb, 1070 ppm REE, 140 ppm Y, and 180 ppm Nb). In some carbonatites, amphiboles contribute as much as 25% of the Zr + Hf, 15% of the Sr and 35% of the Rb + Ba whole-rock budget. Both clinopyroxenes and amphiboles may also host a significant share (~ 10%) of the bulk heavy-REE content. Our trace-element data show that the partitioning of REE between clinopyroxene (and, in some samples, amphibole) and the melt is clearly bimodal and requires a revision of the existing models assuming single-site REE partitioning. Clinopyroxenes and amphiboles from carbonatites exhibit a diversity of zoning patterns that cannot be explained exclusively on the basis of crystal chemistry and relative compatibility of different trace-element in these minerals. Paragenetic analysis indicates that in most cases, the observed zoning patterns develop in response to removal of selected trace elements by phases co-precipitating with clinopyroxene and amphibole (especially magnetite, fluorapatite, phlogopite and pyrochlore). With the exception of magnesiohastingsite–richterite sample from Afrikanda, the invariability of trace-element ratios in the majority of zoned clinopyroxene and amphibole crystals implies that fluids are not involved in the development of zoning in these minerals. The implications of the new trace-element data for mineral exploration targeting REE, Nb and other types of carbonatite-hosted rare-metal mineralization are discussed.     

The Effect of Geomagnetic and Solar Activity on the Distribution of Controlling Pressure Formations in the Northern Hemisphere in Winter

The distribution of controlling pressure formations, occurring in the Northern Hemisphere during the winters (January and February) of the years 1952 – 1996, has been analysed. It was found that the deepening of the Icelandic and Aleutian pressure lows is connected not only with a particular QBO phase and level of geomagnetic activity (Bochníek et al., 1999) but also with a particular level of solar activity.     

Uniaxial creep tests on a morainic material from switzerland

To determine deformation and strength behaviour of a frozen morainic material uniaxial creep tests with constant load on remoulded samples have been carried out.

From the test results an analytical method describing the mechanical behaviour could be found.

In the following the results of this investigation are presented and an analytical solution is derived. In addition, other experimentally determined curves are compared with the calculated ones. For the material tested the proposed method leads to quite satisfactory results and is expected to do so also for other materials.     

A Wave-Front Curvature Approach to Computing Ray Amplitudes in Inhomogeneous Media with Curved Interfaces

A system of three ordinary non-linear first order differential equations is proposed for the computation of the geometrical spreading of the wave front of a seismic body wave in a three-dimensional medium. The variables of the system are the parameters which provide a second order approximation of the wave front.     

Observation of Precipitating Systems over Complex Orography with Meteorological Doppler Radars: A Feasibility Study

Summary  This paper concerns the use of airborne or ground-based Doppler radars to observe precipitating systems over complex orography. As nearly all of the previous experiments involving Doppler radars were conducted over flat surfaces over the continents or the oceans, new techniques are needed firstly to separate ground clutter from meteorological signal and, in the case of airborne Doppler observations, to deduce navigational errors. Secondly, it is necessary to take the atmospheric circulation induced by orography into account in the three-dimensional wind field analysis. Variational techniques are presented to solve these problems. The proposed methods are tested with simulated ground-based and airborne Doppler radar observations for analytic flows over analytic terrains and for numerically simulated wind and reflectivity fields for the Brig event (22 September 1993) of heavy precipitation over the southern flank of the Alps (Cosma and Richard, 1998), and with actual airborne Doppler data relative to weak snow showers over the Rocky Mountains on 12 March 1995. Received March 22, 1999/Revised June 1, 1999     

On Evaluating Characteristics of the Solute Transport in the Arid Vadose Zone

The transport of bromide (Br) under matric heads of 0, ?2, ?5, and ?10 cm using undisturbed soil columns was investigated for understanding the solute transport in arid soils. Undisturbed soil cores were collected at ground surface, directly below where tension infiltrometer measurements were made in the Amargosa Desert, Nevada, United States. Laboratory experiments were conducted by introducing water containing Br tracer into a soil column maintained at steady‐state conditions. The observed data of breakthrough curves (BTC) were well fitted to an one‐region model, except for the cores at saturation, and a core at the matric head of ?5 cm, from which the observed data were better fitted to a two‐region model. Fitted pore water velocities with the one‐region model ranged from 1.2 to 56.6 cm/h, and fitted dispersion coefficients (D) ranged from 2.2 to 100 cm²/h. Results for the core analyzed with the two‐region model indicated that D ranged from 27.6 to 70.9 cm²/h at saturation, and 25.7 cm²/h at the matric head of ?5 cm; fraction of mobile water (β) ranged from 0.18 to 0.65, and mass transfer coefficient (ω) ranged from 0.006 to 0.03. In summary, the water fluxes and Br dispersion coefficients at investigated matric heads were very high due to the coarseness of the soils and possibly due to preferential flow pathways. These high water fluxes and Br dispersion coefficients would lead to a higher risk of deeper leaching accumulating nitrate nitrogen to the groundwater, and have significant effects on the desert ecosystem.