Some thoughts on GAIA and the sulfur cycle

The data hypothesis states that the composition, oxidation reduction state, and temperature of the troposphere are actively regulated by the biota for the biota. One of the early predictions of the Gaia hypothesis was that there should be a sulfur compound made by the biota in the oceans. It would need to be stable enough against oxidation in water to allow its transfer to the air. Either the sulfur compound itself or its atmospheric oxidation product would have to return sulfur from the sea to the land surfaces. The most likely candidate for this role was dimethyl sulfide. Another sulfur compound of interest from a Gaian viewpoint CS2 (carbon disulfide) is discussed. Theories on the production of dimethyl sulfide and carbon disulfide related to the Gaian hypothesis are examined

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random, Gaussian interactions of order p >= 2, and deterministic self-interactions u <= 0. We show that for nonzero u the effect of increasing the order of the interactions is to make the system more cooperative, in the sense that the fraction of extinct species is greatly reduced. Furthermore, we find that for p > 2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.Comment: 7 pages, 4 Postscript figure

Higher dimensional gravity invariant under the Poincare group

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincar\`{e} translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451.Comment: 7 pages, Latex, accepted in Phys. Rev.

Normal frames and the validity of the equivalence principle

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are explicitly described. The holonomicity of the normal bases is considered. The results obtained are applied to the important case of linear connections and their relationship with the equivalence principle is described. In particular, any gravitational theory based on tensor derivations which obeys the equivalence principle along all paths, must be based on a linear connection.Comment: 14 pages, LaTeX 2e, the package amsfonts is neede

Preparation and characterisation of high-density ionic liquids incorporating halobismuthate anions

A range of ionic liquids containing dialkylimidazolium cations and halobismuthate anions ([BiBrxClyIz]− and [Bi2BrxClyIz]−) were synthesised by combining dialkylimidazolium halide ionic liquids with bismuth(III) halide salts. The majority were room temperature liquids, all with very high densities. The neat ionic liquids and their mixtures with 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide were characterised using Densitometry, Viscometry, NMR Spectroscopy, Electrospray Ionisation Mass Spectrometry (ESI), Liquid Secondary Ion Mass Spectrometry (LSIMS), Matrix-assisted Laser Desorption/Ionization Mass Spectrometry (MALDI), X-Ray Photoelectron Spectroscopy (XPS) and Thermogravimetric Analysis (TGA), to establish their speciation and suitability for high-temperature applications

Cosmological dynamics of R^n gravity

A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which are not included and can be found at http://www.mth.uct.ac.za/~peter/R

Kerr-Gauss-Bonnet Black Holes: An Analytical Approximation

Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.Comment: 5 pages, 1 figur