Phase transitions in perturbed stiff-fluid Friedmann-Robertson-Walker cosmological models

We consider one-soliton perturbations of a flat Friedmann-Robertson-Walker (FRW) cosmological model, with an ideal fluid with pressure equal to the energy density (stiff fluid), in the case where the “pole trajectory” parameter is negative, introducing thereby singularities along certain null hypersurfaces. Starting with a metric that approaches asymptotically the FR W background, we show that it is possible to construct an extension through these hypersurfaces such that the energy momentum tensor T_ab is finite and satisfies the energy conditions. The extension is only C₁, providing a sort of “shock front” with continuity in T_ab, that has an associated phase transition from null dust to stiff fluid, the transition being of the form described by CHANDRASEKHAR and XANTHOPOULOS.     

The petrology and tectonic setting of Quaternary—Recent volcanic centres of Lombok and Sumbawa,Sunda arc

In the Sunda arc, only the Bali—Lombok—Sumbawa sector is apparently flanked both north and south by oceanic crust. South of Lombok Island the oceanic crust is probably of Early Cretaceous or Late Jurassic age, whereas the oldest rocks known from Lombok and Sumbawa islands are the Lower Miocene to Pliocene sediments and volcanics of the basement beneath the Quaternary—Recent volcanic centres.Three large active volcanoes form the northern parts of Lombok and Sumbawa. The volcanic rocks of Rindjani on Lombok belong to a basalt—andesite—dacite association, rich in plagioclase and hy- and Q-normative. East of Lombok, the volcanic rocks of Tambora and Sangeang Api on Sumbawa belong to a potassic ne—trachybasalt—trachy-andesite association. All three volcanoes occur only 150–190 km above the active north-dipping Benioff zone.Extinct Quaternary centres occur south of the active volcanoes on Sumbawa. Two of these centres, Soromundi and Sangenges, erupted markedly ne- and lc-normative leucitites together with andesites, dacites and trachybasalts.The volcanic composition—space—time relations in the Lombok—Sumbawa sector of the Sunda arc are not in accordance with the generalized island-arc schemata. Conventionally, potassic ne-mnormative island-arc associations are supposed to occur over the deep part of the Benioff zones, far from the trenches of mature island arcs. The SiO₂|K₂O relations of the Rindjani association are reasonably appropriate for a volcano overlying intermediate Benioff-zone depths, but both the Tambora and the Sangeang Api associations are far more potassic than would be predicted by generalized schemata, and also occur in a relatively young arc sector that apparently has developed only since Miocene time.Basalts, trachybasalts and leucitites from the Lombok—Sumbawa sector have been compared: at similar MgO contents and Mg/(Mg+Fe), the progression from hy- and Q-normative to ne- and lc-normative magmas is not marked by significant enrichment in TiO₂, Na₂O, Zr, Nb and P, but is accompanied by a substantial increase in K₂O, Rb, Sr and LREE, by increasing $\text{K}{}_2\text{O}\text{Na}{}_2\text{O}$ and by decreasing K/Rb.${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratios from Rindjani (0.70386–0.70402) and Tambora (0.70385–0.70389) are very similar and among the lowest for the Sunda arc, but from Sangeang Api (0.70460–0.70500) are significantly higher and more variable in spite of the similar tectonic setting and petrological affinities. ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratios of leucities tend to be higher (0.70488–0.70529).The petrogenesis of the volcanic associations of Lombok and Sumbawa cannot be readily explained. Although even the leucitites display the poverty in TiO₂ that generally characterizes volcanics from simple island-arc tectonic settings, there is very obvious uncoupling within the “incompatible elements”: enrichment in the LIL group (K, Rb, Sr but not Na) is not accompanied by similar behaviour in the group of small highly-charged ions (Ti, Zr, Nb, P). It has proved impossible to model this behaviour without invoking inhomogeneities in the source regions, both in mineralogy and in chemical composition. Similar uncoupling within the incompatible elements has also been reported from basalt groups from the Mid-Atlantic Ridge, may also occur in the Birunga province, and might not arise from processes unique to the island-arc environment.We suggest that a LIL-rich component is being progressively added to the source regions. This component could be incorporated by the crystallization of additional phases such as phlogopite or paragasite. If this component occurs deep within the mantle, it might gain passage to shallower regions either by percolating up the downgoing slab to yield the familiar arc magma zonation, or up substantial cross-arc fractures.     

The changing distribution of sex ratios in the british urban system

The preponderance of females in society has steadily decreased since the last war. This paper uses Metropolitan Economic Labour Areas to examine the differential effect of these changes and suggests associations with retirement migration and increasing female economic activity rates.     

The volatile component of quaternary ignimbrite magmas from the North Island,New Zealand

Ignimbrites from the central North Island consist mainly of glass or its devitrified product (70–95%); their phenocryst mineralogy is varied and includes plag., hyp., ti-mag., ilm., aug., hblende, biot., san., qtz, ol., with accessory apatite, zircon and pyrrhotite. The Fe-Mg minerals can be used to divide the ignimbrites into four groups with hyp.+aug. reflecting high quench temperatures and biot.+hblende +hyp.+aug., low quench temperatures. Oxygen fugacities lie above the QMF buffer curve and even in ignimbrites with low crystal contents the solid phases apparently buffered fO₂. Some ignimbrites contain the assemblage actinolite, gedrite, magnetite and hematite, reflecting post-eruption oxidation. The mineralogy also allows estimation of using pyrrhotite and thence , . The assemblage biotite-sanidine can be used to estimate and thence . Water fugacity is calculated in a variety of ways using both biotite and hornblende as well as the combining reaction . It is high and approaches P _total in most ignimbrites (~4kb) but is lower in unwelded pumice breccias. Comparison of temperature estimates using mineral geothermometers for the various phenocryst phases suggests that the ignimbrite magmas showed temperature differences of 60–100 °C and pressure differences of several kilobars. Individual magma chambers therefore, would have extended over several kilometres vertically. The chemical potential of water may have been constant through the magma.