Equilibrium Thermodynamics of Lattice QCD

Lattice QCD allows us to simulate QCD at non-zero temperature and/or densities. Such equilibrium thermodynamics calculations are relevant to the physics of relativistic heavy-ion collisions. I give a brief review of the field with emphasis on our work.Comment: 15 pages, 9 figures. Talk presented at SCGT06, Nagoya, Japan. Version 2 includes minor modifications to reference work not covered in version

The distribution of Mahler's measures of reciprocal polynomials

We study the distribution of Mahler's measures of reciprocal polynomials with complex coefficients and bounded even degree. We discover that the distribution function associated to Mahler's measure restricted to monic reciprocal polynomials is a reciprocal (or anti-reciprocal) Laurent polynomial on [1,\infty) and identically zero on [0,1). Moreover, the coefficients of this Laurent polynomial are rational numbers times a power of \pi. We are led to this discovery by the computation of the Mellin transform of the distribution function. This Mellin transform is an even (or odd) rational function with poles at small integers and residues that are rational numbers times a power of \pi. We also use this Mellin transform to show that the volume of the set of reciprocal polynomials with complex coefficients, bounded degree and Mahler's measure less than or equal to one is a rational number times a power of \pi.Comment: 13 pages. To be published in Int. J. Math. Math. Sc

Fatigue of friction stir welded 2024-T351 aluminium alloy

Fatigue failure characteristics of friction stir welds in 13mm gauge 2024-T351 plate have been assessed. Failure occurred from either the weld region (nugget/flow arm) or from the material immediately surrounding the weld. Fatigue failure from the surrounding material was essentially conventional, initiating from large S-phase intermetallic particles and growing in a macroscopic mode I manner. Corresponding fatigue lives were seen to be comparable to parent plate and results previously reported for similar welds in thinner plate. Failure over the weld region was identified with discontinuities in the macroscopic flow pattern of the weld flow arm. Subsequent crack growth showed pronounced macroscopic crack deflection around the ‘onion ring’ structure of the weld nugget. The bands making up the onion rings were identified with variations in local hardness levels, consistent with a mechanical contribution to the crack deflection process

The Ginibre ensemble of real random matrices and its scaling limits

We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2 \times 2$ matrix kernel associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.Comment: 47 pages, 8 figure

Permanent-magnet atom chips for the study of long, thin atom clouds

Atom-chip technology can be used to confine atoms tightly using permanently magnetised videotape along with external magnetic fields. The one-dimensional (1D) gas regime can be realised and studied by trapping the atoms in high-aspect-ratio traps in which the radial motion of the system is confined to zero-point oscillation