Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics

Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt's spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban's method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2+1 Maxwell equations on a deformed sphere.Comment: New version matches the published versio

COFFEE -- An MPI-parallelized Python package for the numerical evolution of differential equations

COFFEE (ConFormal Field Equation Evolver) is a Python package primarily developed to numerically evolve systems of partial differential equations over time using the method of lines. It includes a variety of time integrators and finite differencing stencils with the summation-by-parts property, as well as pseudo-spectral functionality for angular derivatives of spin-weighted functions. Some additional capabilities include being MPI-parallelisable on a variety of different geometries, HDF data output and post processing scripts to visualize data, and an actions class that allows users to create code for analysis after each timestep.Comment: 12 pages, 1 figure, accepted to be published in Software

The National Small Wind Turbine Centre

In August 2008, the Federal government announced funding for a National Small Wind Turbine Centre (NSWTC) to be operated by the Research Institute of Sustainable Energy (RISE), based at Murdoch University in Perth, Western Australia. The aim of the NSWTC is to promote the small wind turbine (SWT) market and industry in Australia by providing services in the areas of Testing, Standards and Labelling, Professional Development and Training, and Research. This paper summarises the work that has been carried out to date by the NSWTC in the area of Standards and Labelling. Existing certification and labelling schemes for SWTs are summarised and an overview is given of the NSWTC participation in the International Energy Agency (IEA) Task 27, a task aimed at research that will advance standards, improve the quality of SWT testing around the globe and lead to an international consumer label for SWTs. Options for certification and labelling for the emerging Australian SWT industry are analysed and the idea of introducing an Australian consumer label for SWTs is discussed

Generalised time functions and finiteness of the Lorentzian distance

We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional description of the Lorentzian distance extending the work of Franco and Moretti.Comment: 22 pages. Some imprecisions clarified compared to first versio

Analysis of turbulence and vortex structures by flow mapping

The technique of Particle Image Velocimetry (PIV) flow mapping is reviewed and comparisons made with Laser Doppler Anemometry (LDA). Results are presented showing the application of PlV to the determination of coherent structures in grid-generated turbulence and theoretical expressions are presented for the errors associated with the computation of statistical parameters. Measurements are also presented showing the vortex structure in the wake of a model wind turbine. These studies have revealed fundamental inadequacies in existing computer codes used by the wind turbine industry

A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.Comment: 23 page