Inspired by equivariant homotopy theory, equivariant algebra studies generalisations of G-Mackey functors that do not have all transfer maps (also known as induction maps), for G a finite group. These incomplete Mackey functors have interesting and subtle properties that are more complicated than classical algebra. The levels of incompleteness that occur are indexed by simple combinatorial data known as transfers systems for G, which are refinements of the subgroup relation satisfying certain axioms. The aim of this paper is to generalise the Greenlees-May and Thevenaz-Webb splitting result of rational G-Mackey functors to the incomplete case. By calculating idempotents of the rational incomplete Burnside ring of G, we find maximal splitting of the category of rational incomplete G-Mackey functors. These splittings are determined by maps of the form (H to G) in the transfer system. We give an intrinsic definition of the split pieces beyond the idempotent description in order to understand what is the minimal information needed to determine an arbitrary rational incomplete G-Mackey functor. We end the paper with a series of examples of possible splittings and illustrate how simpler transfer systems have fewer terms in the splitting but the split pieces are more complicated.

David Barnes Michael A. Hill Magdalena Kedziorek

Radio observations of galaxy clusters show that the intra cluster medium is permeated by \mu G magnetic fields. The origin and evolution of these cosmological magnetic fields is currently not well understood and so their impact on the dynamics of structure formation is not known. Numerical simulations are required to gain a greater understanding and produce predictions for the next generation of radio telescopes. We present the galactic chemodynamics smoothed particle magnetohydrodynamic (SPMHD) code (GCMHD+), which is an MHD implementation for the cosmological smoothed particle hydrodynamic code GCD+. The results of 1, 2 and 3 dimensional tests are presented and the performance of the code is shown relative to the ATHENA grid code. GCMHD+ shows good agreement with the reference solutions produced by ATHENA. The code is then used to simulate the formation of a galaxy cluster with a simple primordial magnetic field embedded in the gas. A homogeneous seed field of 10^-11 G is amplified by a factor of 10^3 during the formation of the cluster. The results show good agreement with the profiles found in other magnetic cluster simulations of similar resolution.

David J. Barnes Daisuke Kawata Kinwah Wu

Radio maps at 21 cm of foreground neutral hydrogen over three cooling flow clusters of galaxies show that the foreground gas is uniform on scales from about 1 -- 10 arcmin. Five sigma limits on fluctuations in the foreground column density for Abell 3581, Sersic 159-03 and Abell 2597 are 6.2e19, 7.8e19 and 4.3e19 per sq cm, or 14, 43 and 17 per cent of the mean foreground column density in the region of the system, respectively. Fluctuations in the column density of neutral gas in the Galaxy are unlikely to account for any excesses of photoelectric absorption in these or other cooling flow clusters. Fluctuations in the foreground neutral gas on arcminute scales are also unlikely to be the cause of excess EUV and soft X-ray emission from clusters.

David G. Barnes Paul E. J. Nulsen

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.

David G. Barnes Christopher J. Fluke

The forthcoming generation of radiotelescopes pose new and substantial challenges in terms of system monitoring. Information regarding environmental conditions, signal connectivity and level, processor utilisation, memory use, network traffic and even power consumption needs to be collected, displayed in realtime, and preserved in a permanent database. In this paper, we put forward the Ganglia monitoring system as a scalable, robust and efficient architecture that appears well-suited to the data collection aspect of radiotelescope monitoring, and we discuss approaches to the visual display of the streaming metric data produced by Ganglia. In particular, we present initial work in the use of 3-dimensional (3-d) multiplayer game technology for instantaneous status monitoring and enquiry, and we describe the extensions to this work required for radiotelescope monitoring.

David G. Barnes Grenville Armitage

The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational toral G-spectra for arbitrary compact Lie groups. This paper provides an introduction to the subject in two parts. The first discusses rational G-Mackey functors, the action of the Burnside ring and change of group functors. It gives a complete proof of the well-known classification of rational Mackey functors for finite G. The second part discusses the methods and tools from equivariant stable homotopy theory needed to obtain algebraic models for rational G-spectra. It gives a summary of the key steps in the classification of rational G-spectrain terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to clearly see the analogy between the algebraic and topological classifications.

David Barnes Magdalena Kedziorek

We investigate the in-medium modification of the charmonium breakup processes due to the Mott effect for light (pi, rho) and open-charm (D, D*) quark-antiquark bound states at the chiral/deconfinement phase transition. The Mott effect for the D-mesons effectively reduces the threshold for charmonium breakup cross sections, which is suggested as an explanation of the anomalous J/psi suppression phenomenon in the NA50 experiment. Further implications of finite-temperature mesonic correlations for the hadronization of heavy flavors in heavy-ion collisions are discussed.

D. Blaschke G. Burau Yu. Kalinovsky T. Barnes

We analyze twenty five nearby metal-rich G and late-F dwarfs in order to verify whether the spectroscopic equilibrium (LTE) of iron lines satisfy the observational constraints imposed by the Infrared Flux Method (angular diameters) and Hipparcos parallaxes. The atmospheric parameters derived from iron lines (assuming LTE and employing 1D Kurucz model atmospheres) do not satisfy simultaneously both observational constraints, probably because classical modeling fails to reproduce the detailed line formation of FeI lines.

Jorge Melendez Ivan Ramirez

In this paper, we provide new formulas for determining the coefficients appearing in the asymptotic expansion for the Barnes $G$-function as $n$ tends to infinity for certain classes of asymptotic expansion for the Barnes $G$-function. We remark that our formulas can be used to approximate the coefficients appearing in an asymptotic expansion of the ``random matrix factor" from the Keathing-Snaith conjecture and the coefficients appearing in an asymptotic expansion of the ``L\'evy-Khintchine type representation of the reciprocal of the Barnes $G$-function".

Aziz Issaka

Equipping a non-equivariant topological E_\infty operad with the trivial G-action gives an operad in G-spaces. The algebra structure encoded by this operad in G-spectra is characterised homotopically by having no non-trivial multiplicative norms. Algebras over this operad are called naive-commutative ring G-spectra. In this paper we let G be a finite group and we show that commutative algebras in the algebraic model for rational G-spectra model the rational naive-commutative ring G-spectra.

David Barnes J. P. C. Greenlees Magdalena Kedziorek