Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

Deep drilling at the Siljan Ring impact structure: oxygen-isotope geochemistry of granite

The Siljan Ring is a 362-Ma-old impact structure formed in 1700-Ma-old I-type granites. A 6.8-km-deep borehole provides a vertical profile through granites and isolated horizontal diabase sills. Fluid-inclusion thermometry, and oxygen-isotope compositions of vein quartz, granite, diabase, impact melt, and pseudotachylite, reveal a complex history of fluid activity in the Siljan Ring, much of which can be related to the meteorite impact. In granites from the deep borehole, ¹⁸O values of matrix quartz increase with depth from near 8.0 at the surface to 9.5 at 5760 m depth. In contrast, feldspar ¹⁸O values decrease with depth from near 10 at the surface to 7.1 at 5760 m, forming a pattern opposite to the one defined by quartz isotopic compositions. Values of ¹⁸O for surface granites outside the impact structure are distinct from those in near-surface samples from the deep borehole. In the deep borehole, feldspar coloration varies from brick-red at the surface to white at 5760 m, and the abundances of crack-healing calcite and other secondary minerals decrease over the same interval. Superimposed on the overall decrease in alteration intensity with depth are localized fracture zones at 4662, 5415, and 6044 m depth that contain altered granites, and which provided pathways for deep penetration of surface water. The antithetic variation of quartz and feldspar ¹⁸O values, which can be correlated with mineralogical evidence of alteration, provides evidence for interaction between rocks and impact-heated fluids (100–300° C) in the upper 2 km of the pluton. Penetration of water to depths below 2 km was restricted by a general decrease in impact-fracturing with depth, and by a 60-m-thick diabase sill at 1500 m depth that may have been an aquitard. At depths below 4 km in the pluton, where water/rock ratios were low, oxygen isotopic compositions preserve evidence for limited high-temperature (>500° C) exchange between alkali feldspar and fluids. The high-temperature exchange may have been a post-impact event involving impact-heated fluids, or a post-magmatic event.     

Mudrocks from the Siberian Hypostratotype of the Riphean and Vendian: Chemistry,Sm–Nd Isotope Systematics of Sources,and Formation Stages

Lithology and Mineral Resources - The chemical composition and Nd isotope systematics were obtained for mudrocks (mudstones) from sections of the Siberian hypostratotype of the Riphean and Vendian...     

Causes of Geochemical Diversity of Carbon Dioxide Water in Crystalline Rock Masses

The problem of the diversity of the geochemical types of carbon dioxide waters (CDW) in petrografically and mineralogically uniform crystalline rock masses is solved with allowance made for the effect of different boundary conditions (physicochemical parameters) on the geochemical effect of interaction in the rock–water system. The formation of the entire geochemical spectrum of CDW in crystalline rock masses is shown to be explicable on the basis of a model of interaction in granite–water systems at different mass ratios of reacting rock (S) and water (L), different temperatures T, and equilibrium concentrations of dissolved CO₂ (P _CO2).     

Modeling Lake Ladoga Zoobenthos and Studying Its Role in Phosphorus Exchange at the Water–Bed Interface

A zoobenthos submodel is included in an ecosystem model. The new model is used to assess the role of zoobenthos in the phosphorus exchange at the water–bed interface, in particular, the phosphorus cycle in the water body ecosystem is described more accurately. The calculated zoobenthos distribution over the bed of a lake can be used in modeling the lake ichthyocenoses.     

Late Cretaceous rift-related upwelling and melting of the Trindade starting mantle plume head beneath western Brazil

High mantle potential temperatures and local extension, associated with the Late-Cretaceous impact of the Trindade mantle plume, produced substantial widespread and voluminous magmatism around the northern half of the Paraná sedimentary basin. Our previous studies have shown that, above the central and eastern portions of the postulated impact zone where lithosphere extension is minimal, heat conducted by the plume caused large-scale melting of the more fusible parts of the subcontinental lithospheric mantle beneath the margin of the São Francisco craton and the surrounding Brasilía mobile belt. Here we combine geochemical data and field evidence from the Poxoreu Igneous Province, western Brazil to show how more intense lithospheric extension above the western margin of the postulated impact zone permitted greater upwelling and melting of the Trindade plume than further east. Laser ⁴⁰Ar/³⁹Ar age determinations indicate that rift-related basaltic magmas of the Poxoreu Igneous Province were emplaced at ? 84 Ma. Our detailed geochemical study of the mafic magmas shows that the parental melts underwent polybaric crystal fractionation within the crust prior to final emplacement. Furthermore, some magmas (quartz-normative) appear to have assimilated upper crust whereas others (nepheline- and hypersthene-normative) appear to have been unaffected by open-system crustal magma chamber processes. Incompatible trace element ratios (e.g. chondrite-normalised La/Nb?=?1) and isotopic ratios (⁸⁷Sr/⁸⁶Sr?=?0.704 and ¹⁴³Nd/¹⁴⁴Nd?=?0.51274) of the Hy-normative basalts resemble those of oceanic islands (OIB). We therefore propose that these “OIB-like” magmas were predominantly derived from convecting-mantle-source melts (i.e. Trindade mantle plume). Inverse modelling of rare-earth element (REE) abundances suggests that the initial melts were predominantly generated within the depth range of ?80–100 km, in mantle with a potential temperature of ?1500 °C.