Resonance behaviour and partial averaging in a three-body system with gravitational radiation damping

In a previous investigation, a model of three-body motion was developed which included the effects of gravitational radiation reaction. The aim was to describe the motion of a relativistic binary pulsar that is perturbed by a third mass and look for resonances between the binary and third-mass orbits. Numerical integration of an equation of relative motion that approximates the binary gives evidence of such resonances. These ( m : n ) resonances are defined for the present purposes by the resonance condition,   m ω= 2 n Ω  , where m and n are relatively prime integers and ω and Ω are the angular frequencies of the binary orbit and third-mass orbit (around the centre of mass of the binary), respectively. The resonance condition consequently fixes a value for the semimajor axis a of the binary orbit for the duration of the resonance because of the Kepler relationship  ω= a ^−3/2  . This paper outlines a method of averaging developed by Chicone, Mashhoon and Retzloff, which renders a non-linear system that undergoes resonance capture into a mathematically amenable form. This method is applied to the present system and one arrives at an analytical solution that describes the average motion during resonance. Furthermore, prominent features of the full non-linear system, such as the frequency of oscillation and antidamping, accord with their analytically derived formulae.     

Impact of post-mixing chemical reactions on the major ion chemistry of bulk meltwaters draining the haut glacier d'arolla,valais, Switzerland

Until now, alpine glacial meltwaters have been assumed to consist of two components, dilute quickflow and concentrated delayed flow, the mixing of which has been regarded as chemically conservative for the major dissolved ions and electrical conductivity. Dye tracing results suggest that this two-component model adequately represents the sub-glacial hydrology of the Haut Glacier d'Arolla, Switzerland. However, laboratory dissolution experiments in which various concentrations of glacial rock flour are placed in dilute solutions show that this rock flour is highly reactive and suggest that bulk meltwaters may acquire significant amounts of solute through rapid chemical reactions with suspended sediment which occur after mixing of the two components. This view is supported by detailed analysis of variations in the hydrochemistry of meltwaters draining from the Haut Glacier d'Arolla over three diurnal cycles during the 1989 melt season. Variations in the composition of bulk meltwaters are controlled by two main factors: dilution of the delayed flow component by quickflow, and the extent of post-mixing reactions. The latter depends on the suspended sediment concentration in bulk meltwaters and on the duration of contact between these waters and suspended sediment. Seasonal changes in the magnitude of these factors result in changes in the character and causes of diurnal variations in meltwater chemistry. In June, these variations reflect discharge-related variations in residence time within a distributed subglacial drainage system; in July, when a channelized drainage system exists beneath the lower glacier, they primarily reflect the dilution of delayed flow by quickflow; in August, when suspended sediment concentrations are particularly high, they reflect varying degrees of solute acquisition by post-mixing reactions with suspended sediment that take place in arterial channels at the glacier bed.     

Book review

Mathematical Geosciences -     

On the temperature dependence of the reaction O + NO → NO12

The published data on the temperature dependence of the radiative combination of atomic oxygen with nitric oxide at pressures near 1 torr is examined. Arguments are advanced to suggest that radiation near the cut-off wavelength (～ 3875Å) is coming from the unstabilized activated complex, No¹₂. At 4000Å a positive activation energy of 1 kcal mole^?1 is deduced. Application of this temperature dependence with the rate coefficient at 5200Å is made to airglow measurements in aurora. The deduced NO concentration is about 10⁹ cm^?3, in general agreement with that deduced from the measured NO⁺/O⁺₂ ratio as well as an auroral model prediction.     

PAPPA: Primordial anisotropy polarization pathfinder array

The primordial anisotropy polarization pathfinder array (PAPPA) is a balloon-based instrument to measure the polarization of the cosmic microwave background and search for the signal from gravity waves excited during an inflationary epoch in the early universe. PAPPA will survey a 20° × 20° patch at the North Celestial Pole using 32 pixels in 3 passbands centered at 89, 212, and 302 GHz. Each pixel uses MEMS switches in a superconducting microstrip transmission line to combine the phase modulation techniques used in radio astronomy with the sensitivity of transition-edge superconducting bolometers. Each switched circuit modulates the incident polarization on a single detector, allowing nearly instantaneous characterization of the Stokes I, Q, and U parameters. We describe the instrument design and status.     

Recurrent spring‐fed rivers in a Middle to Late Pleistocene semi‐arid grassland: Implications for environments of early humans in the Lake Victoria Basin,Kenya

The effect of changing palaeoclimate and palaeoenvironment on human evolution during the Pleistocene is debated, but hampered by few East African records directly associated with archaeological sites prior to the Last Glacial Maximum. Middle to Late Pleistocene deposits on the shoreline of eastern Lake Victoria preserve abundant vertebrate fossils and Middle Stone Age arte‐facts associated with riverine tufas at the base of the deposits, which are ideal for palaeoenvironmental reconstructions. New data from tufas identified on Rusinga Island and on the mainland near Karungu, Kenya are provided from outcrop, thin sections, mineralogical, stable isotopic and U‐series dating analyses. Tufa is identified in four sites: Nyamita (94·0 ± 3·3 and 111·4 ± 4·2 ka); Kisaaka, Aringo (455 ± 45 ka); and Obware. The age ranges of these tufa deposits demonstrate that spring‐fed rivers were a recurrent, variably preserved feature on the Pleistocene landscape for ca 360 kyr. Poor sorting of clastic facies from all sites indicates flashy, ephemeral discharge, but these facies are commonly associated with barrage tufas, paludal environments with δ¹³C values of ca 10‰ indicative of C₃ plants and fossil Hippopotamus, all of which indicate a perennial water source. Other tufa deposits from Nyamita, Obware and Aringo have a mixed C₃/C₄ signature consistent with a semi‐arid C₄ grassland surrounding these spring‐fed rivers. The δ¹⁸O values of tufa from Nyamita are on average ca 1‰ more negative than calcite precipitated from modern rainfall in the region, suggesting greater contribution of depleted monsoonal input, similar to the Last Glacial Maximum. Microdebitage and surface‐collected artefacts indicate that early modern humans were utilizing these spring‐fed rivers. The presence of spring?fed rivers would have afforded animals a reliable water source, sustaining a diverse plant and animal community in an otherwise arid environment.