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.     

Food Deserts in the Prairies? Supermarket Accessibility and Neighborhood Need in Edmonton,Canada*

The U.S. and U.K. literatures have discussed “food deserts,” reflecting populated, typically urban, low‐income areas with limited access to full‐service supermarkets. Less is known about supermarket accessibility within Canadian cities. This article uses the minimum distance and coverage methods to determine supermarket accessibility within the city of Edmonton, Canada, with a focus on high‐need and inner‐city neighborhoods. The results show that for 1999 both of these areas generally had higher accessibility than the remainder of the city, but six high‐need neighborhoods had poor supermarket accessibility. We conclude by examining potential reasons for differences in supermarket accessibility between Canadian, U.S., and U.K. cities.     

Some Aspects of Resource Uncertainty and Their Economic Consequences in Assessment of the 1002 Area of the Arctic National Wildlife Refuge

Natural Resources Research - Exploration ventures in frontier areas have high risks. Before committing to them, firms prepare regional resource assessments to evaluate the potential payoffs. With...     

Chasing a 'loose and baggy monster': almshouses and the geography of charity

This paper goes some way towards redressing the lack of geographical literature on charity through exploring the geography of the British domestic charitable sector. The size and geography of the third sector is outlined, followed by an analysis of how almshouses can be understood as inherently geographical and deeply embedded in local social networks of inclusion as well as exclusion.     

Responses of interrill runoff and erosion rates to vegetation change in southern Arizona

Vegetation change, fi-om grassland to shrubland, has occurred over much of the Sonoran and Chihuahuan Deserts during the past century. The effect of this vegetation change on interrill runoff and erosion was examined by conducting rainfall-simulation experiments on large runoff plots on contemporary grassland and shrubland hillslopes. These experiments show that, compared to the grassland, the interrill portions of shrubland hillslopes (1) have higher runoff rates, (2) experience equilibrium runoff conditions much more frequently, (3) exhibit higher overland flow velocities, and (4) are subject to greater rates of erosion. The environmental change that has led to the vegetation change has been relatively minor, but its geomorphic impact has been substantial.     

A modern vision: Eric Lindsay at Armagh

Eric Mervyn Lindsay masterminded the development of Armagh Observatory in the middle of the 20th century, building it into the centre for research and education that it is today. John McFarland recounts Lindsay's story, of how one man's drive and ambition forged international collaborations that presaged today's world of shared research facilities     

Isotopic order, biogeochemical processes, and earth history: Goldschmidt lecture, Davos, Switzerland, August 2002

The impetus to interpret carbon isotopic signals comes from an understanding of isotopic fractionations imposed by living organisms. That understanding rests in turn on studies of enzymatic isotope effects, on fruitful concepts of isotopic order, and on studies of the distribution of ¹³C both between and within biosynthetic products. In sum, these studies have shown that the isotopic compositions of biological products are governed by reaction kinetics and by pathways of carbon flow.Isotopic compositions of individual compounds can indicate specific processes or environments. Examples include biomarkers which record the isotopic compositions of primary products in aquatic communities, which indicate that certain bacteria have used methane as a carbon source, and which show that some portions of marine photic zones have been anaerobic. In such studies, the combination of structural and isotopic lines of evidence reveals relationships between compounds and leads to process-related thinking. These are large steps. Reconstruction of the sources and histories of molecular fossils redeems much of the early promise of organic geochemistry by resolving and clarifying paleoenviron-mental signals. In turn, contemplation of this new information is driving geochemists to study microbial ecology and evolution, oceanography, and sedimentology.