Packing complete multipartite graphs with 4-cycles

In this paper we completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Injury and alcohol: a hospital emergency department study

A pilot survey was undertaken of injury presentations to a public hospital emergency department to determine patterns of alcohol use in this population. Of the 402 injury presentations in the study period, a total of 236 injury cases were interviewed, of whom 45% (n=107) and 29% (n=69) had consumed alcohol 24 and 6 hours prior to injury. Mean age for all injury presentations was 35.1 years, and 32.6 years for alcohol injury cases. For both injury groups, males were significantly younger than females. Recent alcohol ingestion was three times more common among male than female injury presentations, but with females drinking at significantly lower levels. Of males who had consumed alcohol 6 hours prior to injury, nearly 70% were drinking at NHMRC harmful levels and 61% had drunk more than eight standard drinks. Overall, alcohol-involved injury cases commonly occurred among low-income, single males around 30 years of age who were regular heavy drinkers who were drinking heavily in licensed premises prior to their injury, and who sustained injury through intentional harm. In addition, one in five of the alcohol-involved injury cases were aged 15-18 years, i.e. below the legal age of purchase. The high proportion of hazardous and harmful drinkers among those who had consumed alcohol within the last 6 hours, and the injury sample overall, highlights the need for further research to explore the relationship between the occurrence of injury and the drinking patterns and environments associated with injury. Further research is also required to assess the efficacy of early and brief interventions for alcohol and drug use within the emergency ward setting. This information would enable appropriate public health interventions to be initiated.