Asymptotic dynamics of the exceptional Bianchi cosmologies

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.Comment: 15 pages, 6 figures, submitted to Class. Quantum Gra

Integrability and explicit solutions in some Bianchi cosmological dynamical systems

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases

LANDSAT application of remote sensing to shoreline-form analysis

The author has identified the following significant results. LANDSAT imagery of the southern end of Assateague Island, Virginia, was enlarged to 1:80,000 and compared with high altitude (1:130,000) and low altitude (1:24,000) aerial photography in an attempt to quantify change in land area over a nine month period. Change in area and configuration was found with LANDSAT and low altitude photography. Change in configuration, but no change in area was found with high altitude photography. Due to tidal differences at time of image obtention and lack of baseline data, the accuracy of the LANDSAT measurements could not be determined. They were consistent with the measurements from the low altitude photography

The "Business-As-Usual" growth of global primary energy use and carbon dioxide emissions – historical trends and near-term forecasts

We analyse the global primary energy use and total CO2 emissions time series since 1850 and show that their relative growth rates appear to exhibit periodicity with a fundamental timescale of ~60 years and with significant harmonic behaviour. Quantifying the inertia inherent in these dynamics allows forecasting of future "business as usual" energy needs and their associated CO2 emissions. Our best estimates for 2020 are 800 EJ yr−1 for global energy use and 14 Gt yr−1 for global CO2 emissions, with both being above almost all other published forecasts. This suggests the energy and total CO2 emissions landscape in 2020 may be significantly more challenging than currently envisaged

Magmatic intrusions control Io's crustal thickness

Io, the most volcanically active body in the solar system, loses heat through eruptions of hot lava. Heat is supplied by tidal heating and is thought to be transferred through the mantle by magmatic segregation, a mode of transport that sets it apart from convecting terrestrial planets. We present a model that couples magmatic transport of tidal heat to the volcanic system in the crust, in order to determine the controls on crustal thickness, magmatic intrusions, and eruption rates. We demonstrate that magmatic intrusions are a key component of Io's crustal heat balance; around 80% of the magma delivered to the base of the crust must be emplaced and frozen as plutons to match rough estimates of crustal thickness. As magma ascends from a partially molten mantle into the crust, a decompacting boundary layer forms, which can explain inferred observations of a high-melt-fraction region.Comment: Accepted to JGR:Planets. 24 pages inc appendices and references. 7 figure

Self-similar Bianchi models: II. Class B models

In a companion article (referred hearafter as paper I) a detailed study of the simply transitive Spatially Homogeneous (SH) models of class A concerning the existence of a simply transitive similarity group has been given. The present work (paper II) continues and completes the above study by considering the remaining set of class B models. Following the procedure of paper I we find all SH models of class B subjected only to the minimal geometric assumption to admit a proper Homothetic Vector Field (HVF). The physical implications of the obtained geometric results are studied by specialising our considerations to the case of vacuum and $\gamma -$law perfect fluid models. As a result we regain all the known exact solutions regarding vacuum and non-tilted perfect fluid models. In the case of tilted fluids we find the \emph{general }self-similar solution for the exceptional type VI$_{-1/9}$ model and we identify it as equilibrium point in the corresponding dynamical state space. It is found that this \emph{new} exact solution belongs to the subclass of models $n_\alpha ^\alpha =0$, is defined for $\gamma \in (\frac 43,\frac 32)$ and although has a five dimensional stable manifold there exist always two unstable modes in the restricted state space. Furthermore the analysis of the remaining types, guarantees that tilted perfect fluid models of types III, IV, V and VII$_h$ cannot admit a proper HVF strongly suggesting that these models either may not be asymptotically self-similar (type V) or may be extreme tilted at late times. Finally for each Bianchi type, we give the extreme tilted equilibrium points of their state space.Comment: Latex, 15 pages, no figures; to appear in Classical Quantum Gravity (uses iopart style/class files); (v2) minor corrections to match published versio

High resolution imaging at large telescopes

Image recovery at a resolution limited only by diffraction is now possible at large telescopes. The theory of speckle image reconstruction is explained and the current status of a video recording and digitization system for the reconstruction procedure is described. Potential applications of the process when used with very large telescopes are discussed. The constraints on telescope design imposed by these techniques are listed

Dose-response between frequency of breaks in sedentary time and glucose control in type 2 diabetes: a proof of concept study

Objectives This study aimed to investigate dose-response between frequency of breaks in sedentary time and glucose control.DesignRandomised three-treatment, two-period balanced incomplete block trial.MethodsTwelve adults with type 2 diabetes (age, 60 ± 11 years; body mass index, 30.2 ± 4.7 kg/m2) participated in two of the following treatment conditions: sitting for 7 h interrupted by 3 min light-intensity walking breaks every (1) 60 min (Condition 1), (2) 30 min (Condition 2), and (3) 15 min (Condition 3). Postprandial glucose incremental area under the curves (iAUCs) and 21-h glucose total area under the curve (AUC) were measured using continuous glucose monitoring. Standardised meals were provided. Results Compared with Condition 1 (6.7 ± 0.8 mmol L−1 × 3.5 h−1), post-breakfast glucose iAUC was reduced for Condition 3 (3.5 ± 0.9 mmol L−1 × 3.5 h−1, p ˂ 0.04). Post-lunch glucose iAUC was lower in Condition 3 (1.3 ± 0.9 mmol L−1 × 3.5 h−1, p ˂ 0.03) and Condition 2 (2.1 ± 0.7 mmol L−1 × 3.5 h−1, p ˂ 0.05) relative to Condition 1 (4.6 ± 0.8 mmol L−1 × 3.5 h−1). Condition 3 (1.0 ± 0.7 mmol L−1 × 3.5 h−1, p = 0.02) and Condition 2 (1.6 ± 0.6 mmol L−1 × 3.5 h−1, p ˂ 0.04) attenuated post-dinner glucose iAUC compared with Condition 1 (4.0 ± 0.7 mmol L−1 × 3.5 h−1). Cumulative 10.5-h postprandial glucose iAUC was lower in Condition 3 than Condition 1 (p = 0.02). Condition 3 reduced 21-h glucose AUC compared with Condition 1 (p < 0.001) and Condition 2 (p = 0.002). However, post-breakfast glucose iAUC, cumulative 10.5-h postprandial glucose iAUC and 21-h glucose AUC were not different between Condition 2 and Condition 1 (p ˃ 0.05).Conclusions There could be dose-response between frequency of breaks in sedentary time and glucose. Interrupting sedentary time every 15 min could produce better glucose control