In search for a perfect shape of polyhedra: Buffon transformation

For an arbitrary polygon consider a new one by joining the centres of consecutive edges. Iteration of this procedure leads to a shape which is affine equivalent to a regular polygon. This regularisation effect is usually ascribed to Count Buffon (1707-1788). We discuss a natural analogue of this procedure for 3-dimensional polyhedra, which leads to a new notion of affine $B$-regular polyhedra. The main result is the proof of existence of star-shaped affine $B$-regular polyhedra with prescribed combinatorial structure, under partial symmetry and simpliciality assumptions. The proof is based on deep results from spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro

∗\ast-SDYM fields and heavenly spaces: II. Reductions of the ∗\ast-SDYM system

Reductions of self-dual Yang-Mills (SDYM) system for $\ast$-bracket Lie algebra to the Husain-Park (HP) heavenly equation and to sl(N,{\boldmath{C}) SDYM equation are given. An example of a sequence of $su(N)$ chiral fields ($N\geq 2$) tending for $N\to\infty$ to a curved heavenly space is found.Comment: 18 page

Study of physiological tolerance to centrifugation Final report

Physiological effects and acceleration tolerances after weightlessness based on space environment simulation with human centrifuges and bed res

Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure

On a low energy bound in a class of chiral field theories with solitons

A low energy bound in a class of chiral solitonic field theories related the infrared physics of the SU(N) Yang-Mills theory is established.Comment: Plain Latex, 8 pages, no figure

Electromagnetic analysis of arbitrarily shaped pinched carpets

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.Comment: 6 pages, 6 figures, Current Status of Manuscript: 19Apr10 26May10-Sent on appeal;report rcvd 29Dec09 13Apr10-Ed. decision and/or ref. comments to author;response rcvd 04Dec09 21Dec09-Ed. decision and/or ref. comments to author;response rcvd 01Dec09-Transferred from PRL to PRA 18Aug09 30Nov09-Ed.decision and/or ref. comments to author;response rcvd 14Aug09 - Correspondence sent to autho

An industry-level analysis of potential intangible and economic impacts affecting Australian pork producers during an emergency animal disease control program

Emerging and transboundary diseases have been responsible for dramatic impacts on human health, the economy, trade, animal health and biodiversity in Australia and around the world. The Australian pig industry’s health status provides it with a competitive advantage. Freedom from major transboundary diseases – such as foot-and-mouth disease and classical swine fever – secures access to international markets and enables producers to invest in their businesses free from the complication of major disease incursions, ensures the industry’s future sustainability and allows it to meet community standards for food production. Planning for a disease response is driven by many factors. Among these factors, the cost of the response is often the single most important driving factor. However, cost involves more than the actual financial cost of the response. It involves a number of intangible elements and the views of a diverse range of stakeholders. For example, human health, environmental and sociological consequences need to be considered. Currently, a unifying framework for such decision-making is unavailable. Application of a newly developed framework to several diseases that concern the Australian pig industry will facilitate dialogue on what is the best response to minimize the impact of incursions of such diseases. This novel framework for economic analysis of animal health emergencies incorporates risk assessment, tangible and intangible elements and a value-added cost-benefit analysis. These case studies assess the comparability, applicability and accountability of different response actions through producer perspectives. An example of the application of this framework for a disease which threatens the Australian pig industry will be presented

Resummed Quantum Gravity

We present the current status of the a new approach to quantum general relativity based on the exact resummation of its perturbative series as that series was formulated by Feynman. We show that the resummed theory is UV finite and we present some phenomenological applications as well.Comment: 4 pages, 1 figure; presented at ICHEP0