The mathematical research of William Parry FRS

In this article we survey the mathematical research of the late William (Bill) Parry, FRS

A Survey of Spherically Symmetric Spacetimes

We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-areal coordinates and its properties. In particular, we show how the metric component functions chosen are extremely compatible with notions in Newtonian mechanics. We also show the monotonicity of the Hawking mass in these coordinates. As an example, we discuss how these coordinates and the metric can be used to solve the spherically symmetric Einstein-Klein-Gordon equations. We conclude with a brief mention of some applications of these properties.Comment: 27 pages, 1 figure, Analysis and Mathematical Physics, 201

Very Large Spectroscopic Surveys with the VLT

Recently, it has been recognised that very large spectroscopic surveys (several million spectra) are required to advance our understanding of Dark Energy (via baryonic wiggles) and the detailed history of our Local Group of galaxies (via Galactic Archeology or near-field cosmology). In this paper I make a preliminary exploration of how this might be done by putting a wide field, optical, prime-focus fibre-fed spectroscopic facility on one of the VLT's UTs.Comment: 6 pages. To be published in the proceedings "Science with the VLT in the ELT era

China's new corporate rescue laws: perspectives and principles

This article considers the new corporate insolvency legislation that came into force in China in June 2007. This law is part of a remarkable transformation in the Chinese economy in recent years. Significant numbers of ailing state owned enterprises have been reformed and subjected to hard budgetary constraints, while the private sector has grown dramatically. Market forces play a greater role, whereas the economy was previously tightly controlled by the state. These changes, together with pressures arising from external bodies such as the European Union, led to an urgent need for the adoption of the revised insolvency law, which has at its heart corporate rescue procedures. This article considers the content of this new law, the background to it, and also assesses the prospects for its operation. In particular attention is paid to the level of scope for state interference in the operation of the law

Correlation function algebra for inhomogeneous fluids

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z=0 and z=L respectively) and focus on the structure of the pair correlation function G(r_1,r_2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(z_\mu, z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2 and z_3. These relations form an algebra which severely restricts the possible form of the function G_0(z_\mu,z_\nu). For the common situations in which the equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an odd or even reflection symmetry in the z=L/2 plane the algebra simplifies considerably and is used to relate the correlation function to the finite-size excess free-energy \gamma(L). We rederive non-trivial scaling expressions for the finite-size contribution to the free-energy at bulk criticality and for systems where large scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte

A Comparison of Three Curve Intersection Algorithms

An empirical comparison is made between three algorithms for computing the points of intersection of two planar Bezier curves. The algorithms compared are: the well known Bezier subdivision algorithm, which is discussed in Lane 80; a subdivision algorithm based on interval analysis due to Koparkar and Mudur; and an algorithm due to Sederberg, Anderson and Goldman which reduces the problem to one of finding the roots of a univariate polynomial. The details of these three algorithms are presented in their respective references

Interfacial Structural Changes and Singularities in Non-Planar Geometries

We consider phase coexistence and criticality in a thin-film Ising magnet with opposing surface fields and non-planar (corrugated) walls. We show that the loss of translational invariance has a strong and unexpected non-linear influence on the interface structure and phase diagram. We identify 4 non-thermodynamic singularities where there is a qualitative change in the interface shape. In addition, we establish that at the finite-size critical point, the singularity in the interface shape is characterized by two distint critical exponents in contrast to the planar case (which is characterised by one). Similar effects should be observed for prewetting at a corrugated substrate. Analogy is made with the behaviour of a non-linear forced oscillator showing chaotic dynamics.Comment: 13 pages, 3 figure

A comparative analysis of parallel processing and super-individual methods for improving the computational performance of a large individual-based model

Individual-based modelling approaches are being used to simulate larger complex spatial systems in ecology and in other fields of research. Several novel model development issues now face researchers: in particular how to simulate large numbers of individuals with high levels of complexity, given finite computing resources. A case study of a spatially-explicit simulation of aphid population dynamics was used to assess two strategies for coping with a large number of individuals: the use of ‘super-individuals’ and parallel computing. Parallelisation of the model maintained the model structure and thus the simulation results were comparable to the original model. However, the super-individual implementation of the model caused significant changes to the model dynamics, both spatially and temporally. When super-individuals represented more than around 10 individuals it became evident that aggregate statistics generated from a super-individual model can hide more detailed deviations from an individual-level model. Improvements in memory use and model speed were perceived with both approaches. For the parallel approach, significant speed-up was only achieved when more than five processors were used and memory availability was only increased once five or more processors were used. The super-individual approach has potential to improve model speed and memory use dramatically, however this paper cautions the use of this approach for a density-dependent spatially-explicit model, unless individual variability is better taken into account

Pricing externalities from passenger transportation in Mexico city

The Mexico City Metropolitan Area has been suffering severely from transportation externalities such as accidents, air pollution, and traffic congestion. This study examines pricing instruments to reduce these externalities using an analytical and numerical model. The study shows that the optimal levels of a gasoline tax and a congestion toll on automobiles could generate social benefits, measured in terms of welfare gain, of US$132 and US$109 per capita, respectively, through the reduction of externalities. The largest component of the welfare gains comes from reduced congestion, followed by local air pollution reduction. The optimal toll and tax would, however, double the cost of driving and could be politically sensitive. Still, more than half of those welfare gains could be obtained through a more modest tax or toll, equivalent to $1 per gallon of gasoline. The welfare gains from reforming the pricing of public transportation are small relative to those from reforming the taxation of automobiles. Although the choice among travel modes depends on specific circumstances, in the absence of road travel pricing that accounts for externalities, there will be potential for higher investment in roads relative to mass transit. Given the rapidly increasing demand for transportation infrastructure in Mexico City, careful efforts should be made to include the full social costs of travel in evaluating alternative infrastructure investments.Transport Economics Policy&Planning,Roads&Highways,Energy Production and Transportation,Transport and Environment,Transport in Urban Areas