The low energy effective Lagrangian for photon interactions in any dimension

The subject of low energy photon-photon scattering is considered in arbitrary dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalisation resolves the structure of the weak-field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related, not only to the space-time dimension, but also to the coefficients of the Bernoulli polynomial.Comment: In the revised version, the results have been expressed in terms of Bernoulli polynomials instead of generalized zeta functions; they agree for spinor QED with those of Schubert and Schmidt (obtained differently by path integral methods)

Impact of basidiomycete fungi on the wettability of soil contaminated with a hydrophobic polycyclic aromatic hydrocarbon

Polyaromatic hydrocarbons (PAHs) present a challenge to bioremediation because they are hydrophobic, thus influencing the water availability and repellency of soil. The addition of different concentrations of the PAH, anthracene, showed it to induce moderate levels of repellency. We investigated the efficacy of three basidiomycete fungal species on improving the wettability of soil by reducing repellency caused by contamination of soil with 7 ppm anthracene. A microcosm system was used that enabled determination of the impact of fungi on wettability at three locations down a 30 mm deep repacked soil core. Before incubation with fungi, the contaminated soil had a repellency of R = 3.12 ± 0.08 (s.e.). After 28 days incubation, Coriolus versicolor caused a significant reduction in repellency to R = 1.79 ± 0.35 (P <0.001) for the top section of the soil in a microcosm. Phanerochaete chrysosporium and Phlebia radiata did not influence repellency. None of the fungi had an effect at 20 mm depth

A simple reactive-transport model of calcite precipitation in soils and other porous media

Calcite formation in soils and other porous media generally occurs around a localised source of reactants, such as a plant root or soil macro-pore, and the rate depends on the transport of reactants to and from the precipitation zone as well as the kinetics of the precipitation reaction itself. However most studies are made in well mixed systems, in which such transport limitations are largely removed. We developed a mathematical model of calcite precipitation near a source of base in soil, allowing for transport limitations and precipitation kinetics. We tested the model against experimentally-determined rates of calcite precipitation and reactant concentration–distance profiles in columns of soil in contact with a layer of HCO3−-saturated exchange resin. The model parameter values were determined independently. The agreement between observed and predicted results was satisfactory given experimental limitations, indicating that the model correctly describes the important processes. A sensitivity analysis showed that all model parameters are important, indicating a simpler treatment would be inadequate. The sensitivity analysis showed that the amount of calcite precipitated and the spread of the precipitation zone were sensitive to parameters controlling rates of reactant transport (soil moisture content, salt content, pH, pH buffer power and CO2 pressure), as well as to the precipitation rate constant. We illustrate practical applications of the model with two examples: pH changes and CaCO3 precipitation in the soil around a plant root, and around a soil macro-pore containing a source of base such as urea