Dynamical Models for the Formation of Elephant Trunks in H II Regions

The formation of pillars of dense gas at the boundaries of H II Regions is investigated with hydrodynamical numerical simulations including ionising radiation from a point source. We show that shadowing of ionising radiation by an inhomogeneous density field is capable of forming so-called elephant trunks (pillars of dense gas as in e.g. M16) without the assistance of self-gravity, or of ionisation front and cooling instabilities. A large simulation of a density field containing randomly generated clumps of gas is shown to naturally generate elephant trunks with certain clump configurations. These configurations are simulated in isolation and analysed in detail to show the formation mechanism and determine possible observational signatures. Pillars formed by the shadowing mechanism are shown to have rather different velocity profiles depending on the initial gas configuration, but asymmetries mean that the profiles also vary significantly with perspective, limiting their ability to discriminate between formation scenarios. Neutral and molecular gas cooling are shown to have a strong effect on these results.Comment: 17 pages, 11 figures, MNRAS. Minor revisions: typos corrected, figures re-ordered to match published versio

U-duality in three and four dimensions

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references added; v3: further discussion added on the conformal factor of the generalised metric in section 2 and on the Wick-rotation used to construct examples in section

On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

Towards an Indigenous Leadership Paradigm for Dismantling Ableism

The purpose of this article is to propose an Indigenous leadership paradigm for dismantling ableism. I begin by defining ableism within the context of school leadership, then apply an Indigenous ontological and epistemological framework to strategies educational leaders can use to dismantle cultures of ableism within school communities