Characteristics and classification of A-type supergiants in the Small Magellanic Cloud

We address the relationship between spectral type and physical properties for A-type supergiants in the SMC. We first construct a self-consistent classification scheme for A supergiants, employing the calcium K to H epsilon line ratio as a temperature-sequence discriminant. Following the precepts of the `MK process', the same morphological criteria are applied to Galactic and SMC spectra with the understanding there may not be a correspondence in physical properties between spectral counterparts in different environments. We then discuss the temperature scale, concluding that A supergiants in the SMC are systematically cooler than their Galactic counterparts at the same spectral type, by up to ~10%. Considering the relative line strengths of H gamma and the CH G-band we extend our study to F and early G-type supergiants, for which similar effects are found. We note the implications for analyses of extragalactic luminous supergiants, for the flux-weighted gravity-luminosity relationship and for population synthesis studies in unresolved stellar systems.Comment: 14 pages, 14 figures, accepted by MNRAS; minor section removed prior to final publicatio

Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

Making a national atlas of population by computer

This paper describes the conceptual and practical problems encountered and solved in producing a multi-colour atlas of population characteristics in Great Britain. The atlas itself is in A4 format; it consists of some thirty-four maps of Great Britain in four colours and the same number of regional maps, together with descriptive text. All maps were plotted on a laser plotter with a resolution of 127 microns. The paper describes how mapping of ratios, such as percentages, was found to be highly misleading and describes the novel probability mapping solution adopted, based on the signed chi-square statistic. In addition, the rationale for selecting the class intervals and for selecting colour schemes is described

Smilansky's model of irreversible quantum graphs, II: the point spectrum

In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of K one-dimensional oscillators attached at different points of the graph. This paper is a continuation of our investigation of the case K>1. For the sake of simplicity we consider K=2, but our argument applies to the general situation. In this second paper we apply the variational approach to the study of the point spectrum.Comment: 18 page

SLS Materials Development Method for Rapid Manufacturing

As soon as SFF technology development began to make Rapid Prototyping possible the interest in Rapid Manufacturing (RM) began to grow. The advantages in terms of functional integration, elimination of tooling and fixtures and mass customization make a compelling case for RM, leading some in the field to call it the next industrial revolution. Yet without the materials properties necessary to provide the function and variety currently available from mass production methods, the application of RM will remain limited. Developing new materials for the SLS process, one immediate step toward a larger portfolio of RM materials, is very challenging. The formation of high quality SLS parts relies on appropriate powder characteristics, thermal cycles and sintering behavior. Based on a brief examination of the key factors in SLS processing and a research project to develop a new binder material for Silicon Carbide composites, a systematic materials development method is proposed in this paper. The method provides guidance for introducing new SLS materials, support for educating new SLS users and researchers and direction for several future research projects.Mechanical Engineerin

Rapid Manufacturing of Silicon Carbide Composites

From the earliest days of SFF technology development, a viable technique for the direct manufacture of fully-functional parts has been a major technology goal. While direct metal methods have been demonstrated for a variety of metals including aluminum, steel and titanium, they have not reached wide commercial application due to processing speed, final material properties and surface finish. In this paper the development of an SLS-based rapid manufacturing (RM) platform is reviewed. The core of this platform is a thermosetting binder system for preform parts in contrast to the thermoplastic materials currently available for SLS. The preforms may include metal and/or ceramic powders. A variety of fully functional parts can be prepared from different combinations of materials and post processing steps including binder pyrolysis, free-standing alloy infiltration, room temperature polymer infiltration and machining. The main issues of these steps are reviewed followed by a discussion about the support of RM. This paper is an intermediate report additional materials, applications, process models and product design strategies will be incorporated into the project in the next year.Mechanical Engineerin

Kinetic pathways of multi-phase surfactant systems

The relaxation following a temperature quench of two-phase (lamellar and sponge phase) and three-phase (lamellar, sponge and micellar phase) samples, has been studied in an SDS/octanol/brine system. In the three-phase case we have observed samples that are initially mainly sponge phase with lamellar and micellar phase on the top and bottom respectively. Upon decreasing temperature most of the volume of the sponge phase is replaced by lamellar phase. During the equilibriation we have observed three regimes of behaviour within the sponge phase: (i) disruption in the sponge texture, then (ii) after the sponge phase homogenises there is a lamellar nucleation regime and finally (iii) a bizarre plume connects the lamellar phase with the micellar phase. The relaxation of the two-phase sample proceeds instead in two stages. First lamellar drops nucleate in the sponge phase forming a onion `gel' structure. Over time the lamellar structure compacts while equilibriating into a two phase lamellar/sponge phase sample. We offer possible explanatioins for some of these observations in the context of a general theory for phase kinetics in systems with one fast and one slow variable.Comment: 1 textfile, 20 figures (jpg), to appear in PR

A Geometric, Dynamical Approach to Thermodynamics

We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself micro-canonically observable. In particular, temperature, specific heat and higher order derivatives of the entropy can be observed dynamically. We give perturbative, asymptotic formulas by which the canonical ensemble itself can be reconstructed from micro-canonical measurements only. In a purely micro-canonical approach we rederive formulas by Lebowitz et al \cite{LPV}, relating e.g. specific heat to fluctuations in the kinetic energy. We show that under natural assumptions on the fluctuations in the kinetic energy the micro-canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy.Comment: 7 pages, LaTeX, uses RevTex. New sections and examples using fluctuations in the kinetic energy adde

Birds and people in Europe

At a regional scale, species richness and human population size are frequently positively correlated across space. Such patterns may arise because both species richness and human density increase with energy availability. If the species-energy relationship is generated through the 'more individuals' hypothesis, then the prediction is that areas with high human densities will also support greater numbers of individuals from other taxa. We use the unique data available for the breeding birds in Europe to test this prediction. Overall regional densities of bird species are higher in areas with more people; species of conservation concern exhibit the same pattern. Avian density also increases faster with human density than does avian biomass, indicating that areas with a higher human density have a higher proportion of small-bodied individuals. The analyses also underline the low numbers of breeding birds in Europe relative to humans, with a median of just three individual birds per person, and 4 g of bird for every kilogram of human