Non-radial stellar oscillations: a perspective from potential scattering (I)

This article is the first in a series designed to gain insight into the stellar oscillation problem from a somewhat novel point of view: that of potential scattering, well-known in the quantum mechanical literature. In this paper the known theoretical foundations are developed and applied in the context of the astrophysical problem, wherein the star itself (rather than any portion of it) is the potential which scatters waves and traps them. The basis for the identification of a precisely defined scattering problem is the existence of a linear Schrödinger equation associated both globally (Section 2) and locally (Section 8) with the nonlinear eigenvalue equation for nonradial stellar pulsations. The paper is also designed to be a fairly complete account of the relevant mathematical topics that are germane to a study of this kind. This paper is dedicated to the memory of Professor Zdenèk Kopal, who was a great source of professional encouragement to me during the last fifteen years of his life.     

Precambrian fluvial deposits: Enigmatic palaeohydrological data from the c. 2–1.9 Ga Waterberg Group, South Africa

Precambrian fluvial systems, lacking the influence of rooted vegetation, probably were characterised by flashy surface runoff, low bank stability, broad channels with abundant bedload, and faster rates of channel migration; consequently, a braided fluvial style is generally accepted. Pre-vegetational braided river systems, active under highly variable palaeoclimatic conditions, may have been more widespread than are modern, ephemeral dry-land braided systems. Aeolian deflation of fine fluvial detritus does not appear to have been prevalent. With the onset of large cratons by the Neoarchaean–Palaeoproterozoic, very large, perennial braided river systems became typical. The c. 2.06–1.88 Ga Waterberg Group, preserved within a Main and a smaller Middelburg basin on the Kaapvaal craton, was deposited largely by alluvial/braided-fluvial and subordinate palaeo-desert environments, within fault-bounded, possibly pull-apart type depositories.

Palaeohydrological data obtained from earlier work in the Middelburg basin (Wilgerivier Formation) are compared to such data derived from the correlated Blouberg Formation, situated along the NE margin of the Main basin. Within the preserved Blouberg depository, palaeohydrological parameters estimated from clast size and cross-bed set thickness data, exhibit rational changes in their values, either in a down-palaeocurrent direction, or from inferred basin margin to palaeo-basin centre. In both the Wilgerivier and Blouberg Formations, calculated palaeoslope values (derived from two separate formulae) plot within the gap separating typical alluvial fan gradients from those which characterise rivers (cf. [Blair, T.C., McPherson, J.G., 1994. Alluvial fans and their natural distinction from rivers based on morphology, hydraulic processes, sedimentary processes, and facies assemblages. J. Sediment. Res. A64, 450–489.]). Although it may be argued that such data support possibly unique fluvial styles within the Precambrian, perhaps related to a combination of major global-scale tectono-thermal and atmospheric–palaeoclimatic events, a simpler explanation of these apparently enigmatic palaeoslope values may be pertinent. Of the two possible palaeohydrological formulae for calculating palaeoslope, one provides results close to typical fluvial gradients; the other formula relies on preserved channel-width data. We suggest that the latter will not be reliable due to problematic preservation of original channel-widths within an active braided fluvial system. We thus find no unequivocal support for a unique fluvial style for the Precambrian, beyond that generally accepted for that period and discussed briefly in the first paragraph.     

Glacial Erosion in the Abisko Mountains: Kärkevagge and Vassivagge, Northern Sweden

This paper discusses direct current resistivity soundings and geomorphological studies of Quaternary deposits in two glacial troughs in the Abisko Mountains of northern Sweden. The subject of the fieldwork is the depth of Pleistocene glacial erosion. Studies were carried out in 1998 and 2003 in the Kärkevagge and Vassivagge. The estimated thickness of Quaternary deposits and bedrock properties are discussed in the broader context of glacial erosion studies in the Abisko area. Geophysical and geomorphological studies suggest that the depth of glacial erosion was highly differentiated from –190 m in the Torneträsk basin to the metric overall erosion on the upland plateau. In medium‐sized valleys several kilometres long, erosion depth measures 30–50 m. Present‐day stream channel patterns reveal a strong relation to the bedrock configuration in valley floors     

Redbed-type gold mineralisation, Kupferschiefer, south-west Poland

A new type of gold mineralisation containing minor amounts of platinum and palladium has been found proximal to the secondary redox interface located below the Cu-Ag Kupferschiefer orebody of the Polkowice-Sieroszowice mine in the south-western part of the Lubin-Sieroszowice district, Poland. This deposit can be classified as redbed-type gold. Our study shows that gold, platinum and palladium occur in secondary red-coloured sections of the basal Zechstein sedimentary rocks and in the uppermost Weissliegendes sandstone. Noble metal mineralisation occurs within an average interval of 0.22 m, which lies directly below the copper ores. The average grade of the horizon is 2.25 ppm Au, 0.138 ppm Pt and 0.082 ppm Pd with a metal content of several tens of tonnes of gold. A transition zone has been recognised between the gold-bearing horizon and the copper deposit. This transition zone is characterised by the presence of low grades of copper (<0.2 wt%) and elevated gold contents (>0.5 ppm). Native gold accompanied by electrum, mercury-bearing gold, haematite, covellite, chalcocite, bornite and chalcopyrite has been identified in the gold-bearing horizon. In some sections, Pd-arsenides, tetra-auricupride, Co-arsenides, clausthalite, tennantite, digenite, yarrowite, spionkopite and galena have also been noted.     

Rates of Deglaciation during the Last Glaciation and Holocene in the Cordillera Vilcanota-Quelccaya Ice Cap Region, Southeastern Perú

Moraine chronology is combined with digital topography to model deglacial rates of paleoglacier volumes in both the Huancané Valley on the west side of the Quelccaya Ice Cap and the Upismayo Valley on the northwest side of the Cordillera Vilcanota. The fastest rates of deglaciation (39×10⁻⁵ to 114×10⁻⁵ km³ yr⁻¹ and 112×10⁻⁵ to 247×10⁻⁵ km³ yr⁻¹ for each valley, respectively) were calculated for the most recent paleoglaciers, corresponding to the last few centuries. These results are consistent with observations in the Venezuelan Andes showing high rates of deglaciation since the Little Ice Age. These rates also fall within the range of 20th century rates of deglaciation measured on the Quelccaya Ice Cap (29×10⁻⁵ to 220×10⁻⁵ km³ yr⁻¹, Brecher and Thompson, 1993; Thompson, 2000). These results imply that rates of deglaciation may fluctuate significantly over time and that high rates of deglaciation may not be exclusive to the late 20th century. Equilibrium line altitude (ELA) depressions for the ice volumes of the last glaciation modeled here were computed as 230 m for the Quelccaya Ice Cap and 170 m for the Cordillera Vilcanota. Maximum ELA depressions are lower than previously published: <500 m for the Cordillera Vilcanota and <400 m for the Quelccaya Ice Cap. These lower values could imply a topographic control over paleoglacier extent.     

Analyzing CO2 emissions mitigation by technology improvement in Central and Eastern Europe

As a legacy of the centrally planned economy, the economies in transition of Central and Eastern Europe (CEE) have a unique potential to reduce their greenhouse gas emissions through the improvement in their high energy intensities. Since much of this `low-hanging fruit' in energy-efficiency improvements can be highly cost-effective, many developed countries facing difficulties in meeting their greenhouse gas (GHG) emission targets domestically are eager to find such opportunities in the CEE region. Therefore, studies analysing the potentials and costs of carbon dioxide reduction through technology improvement in the region have come into the limelight. While there are a few excellent studies in the region aimed at analysing climate change abatement potentials, they all embark on different assumptions, methodologies and boundary conditions. It is hence difficult, if not impossible, to compare and analyse the results of these studies across different authors, countries or time horizons. Consequently, the purpose of this paper is to place four leading studies on GHG mitigation through technology improvement from the CEE region into an internationally comparable framework. Four studies were selected from three countries, Poland, Hungary and Estonia, which are all the results of major national and international efforts to assess costs and potentials of GHG reduction. The paper places their assumptions, methods and final results into a framework which enables policy-makers and project designers to compare these across geographical and technological boundaries. Since other studies from around the globe have been analysed in this framework in the literature, this paper provides a vehicle for the findings of these four studies to be compared to others worldwide. In addition, the paper highlights a few areas where similar studies to be completed in the future in the region may be enhanced by incorporating features used in GHG mitigation research in other parts of the world. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pressure effect on Ti- or P-rich accessory mineral saturation in evolved granitic melts with differing K2O/Na2O ratios

The solubility of Ti- and P-rich accessory minerals has been examined as a function of pressure and K₂O/Na₂O ratio in two series of highly evolved silicate systems. These systems correspond to (a) alkaline, varying from alkaline to peralkaline with increasing K₂O/Na₂O ratio; and (b) strongly metaluminous (essentially trondhjemitic at the lowest K₂O/Na₂O ratio) and remaining metaluminous with increasing K₂O/Na₂O ratio (to 3). The experiments were conducted at a fixed temperature of 1000 °C, with water contents varying from 5 wt.% at low pressure (0.5 GPa), increasing through 5–10 wt.% at 1.5–2.5 GPa to 10 wt.% at 3.5 GPa. Pressure was extended outside the normal crustal range, so that the results may also be applied to derivation of hydrous silicic melts from subducted oceanic crust.

For the alkaline composition series, the TiO₂ content of the melt at Ti-rich mineral saturation decreases with increasing pressure but is unchanged with increasing K content (at fixed pressure). The P₂O₅ content of the alkaline melts at apatite saturation increases with increased pressure at 3.5 GPa only, but decreases with increasing K content (and peralkalinity). For the metaluminous composition series (termed as “trondhjemite-based series” (T series)), the TiO₂ content of the melt at Ti-rich mineral saturation decreases with increasing pressure and with increasing K content (at fixed pressure). The P₂O₅ content of the T series melts at apatite saturation is unchanged with increasing pressure, but decreases with increasing K content. The contrasting results for P and Ti saturation levels, as a function of pressure in both compositions, point to contrasting behaviour of Ti and P in the structure of evolved silicate melts. Ti content at Ti-rich mineral saturation is lower in the alkaline compared with the T series at 0.5 GPa, but is similar at higher pressures, whereas P content at apatite saturation is lower in the T series at all pressures studied. The results have application to A-type granite suites that are alkaline to peralkaline, and to I-type metaluminous suites that frequently exhibit differing K₂O/Na₂O ratios from one suite to another.     

The rate of grain release by pore-ice sublimation in cold-aeolian environments

Pore‐ice sublimation is a prerequisite for aeolian activity in cold environments where surface sediments hold significant amounts of frozen water. Few quantitative studies have defined the rate of grain release from cemented surfaces by pore‐ice sublimation. In 1996–1997, controlled field experiments at Presqu'ile Beach, Ontario, were implemented to measure sediment release from frozen surfaces. The release rates were compared to the local wind regime, ambient temperature and humidity. In additional field experiments, the effect of sediment water content on grain release by sublimation was examined. From the experimental results, an equation which predicts grain release based on local wind speed, ground temperature, humidity, and surface water content is proposed. Predicted release rates show reasonable agreement with natural deflation measured on the beach at Presqu'ile Provincial Park.     

Tsunami Hazard and Risk in Canada

Tsunamis have occurred in Canada due to earthquakes, landslides, and a large chemical explosion. The Pacific coast is at greatest risk from tsunamis because of the high incidence of earthquakes and landslides in that region. The most destructive historical tsunamis, however, have been in Atlantic Canada – one in 1917 in Halifax Harbour, which was triggered by a catastrophic explosion on a munitions ship, and another in 1929 in Newfoundland, caused by an earthquake-triggered landslide at the edge of the Grand Banks. The tsunami risk along Canada's Arctic coast and along the shores of the Great Lakes is low in comparison to that of the Pacific and Atlantic coasts. Public awareness of tsunami hazard and risk in Canada is low because destructive tsunamis are rare events.