Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

An investigation into regional differences in educational performance in the National Child Development Study

The National Child Development Study (NCDS) is used to investigate factors which affect children's educational performance over time. Multilevel modelling techniques are used on a subset of the NCDS to investigate variation in educational performance in 11 regions in the UK, and in local education authorities within these regions. Social characteristics of the NCDS members are also analysed. Differences between regions and education authorities are found to be negligible, the main source of variation in achievement being due to differences in social background.

An experimental and numerical CFD study of turbulence in a tundish container

This paper describes work performed at IRSID/USINOR in France and the University of Greenwich, UK, to investigate flow structures and turbulence in a water-model container, simulating aspects typical of metal tundish operation. Extensive mean and fluctuating velocity measurements were performed at IRSID using LDA to determine the flow field and these form the basis for a numerical model validation. This apparently simple problem poses several difficulties for the CFD modelling. The flow is driven by the strong impinging jet at the inlet. Accurate description of the jet is most important and requires a localized fine grid, but also a turbulence model that predicts the correct spreading rates of jet and impinging wall boundary layers. The velocities in the bulk of the tundish tend to be (indeed need to be) much smaller than those of the jet, leading to damping of turbulence, or even laminar flow. The authors have developed several low-Reynolds number (low-Re) k–var epsilon model variants to compute this flow and compare against measurements. Best agreement is obtained when turbulence damping is introduced to account not only for walls, but also for low-Re regions in the bulk – the k–var epsilon model otherwise allows turbulence to accumulate in the container due to the restricted outlet. Several damping functions are tested and the results reported here. The k–ω model, which is more suited to transitional flow, also seems to perform well in this problem.

Experimental and numerical study of the cold crucible melting process

The cold crucible, or induction skull melting process as is otherwise known, has the potential to produce high purity melts of a range of difficult to melt materials, including Ti–Al and Ti6Al4V alloys for Aerospace, Ti–Ta and other biocompatible materials for surgical implants, silicon for photovoltaic and electronic applications, etc. A water cooled AC coil surrounds the crucible causing induction currents to melt the alloy and partially suspend it against gravity away from water-cooled surfaces. Strong stirring takes place in the melt due to the induced electromagnetic Lorentz forces and very high temperatures are attainable under the right conditions (i.e., provided contact with water cooled walls is minimised). In a joint numerical and experimental research programme, various aspects of the design and operation of this process are investigated to increase our understanding of the physical mechanisms involved and to maximise process efficiency. A combination of FV and Spectral CFD techniques are used at Greenwich to tackle this problem numerically, with the experimental work taking place at Birmingham University. Results of this study, presented here, highlight the influence of turbulence and free surface behaviour on attained superheat and also discuss coil design variations and dual frequency options that may lead to winning crucible designs.

A study of modelling approaches for rail vehicle collision behaviour

A rigid wall model has been used widely in the numerical simulation of rail vehicle impacts. Finite element impact modelling of rail vehicles is generally based on a half-width and full-length or half-length structure, depending on the symmetry. The structure and components of rail vehicles are normally designed to cope with proof loading to ensure adequate ride performance. In this paper, the authors present a study of a rail vehicle with driving cab focused on improving the modelling approach and exploring the intrinsic structural weaknesses to enhance its crashworthiness. The underpinning research used finite element analysis and compared the behaviour of the rail vehicle in different impact scenarios. It was found that the simulation of a rigid wall impact can mask structural weaknesses; that even a completely symmetrical impact may lead to an asymmetrical result; that downward bending is an intrinsic weakness of conventional rail vehicles and that a rigid part of the vehicle structure, such as the body bolster, may cause uncoordinated deformation and shear fracture between the vehicle sections. These findings have significance for impact simulation, the full-scale testing of rail vehicles and rail vehicle design in general.

Reliability study of the electroless Ni–P layer against solder alloy

Copper (Cu) has been widely used in the under bump metallurgy of chip and substrate metallization for chip packaging. However, due to the rapid formation of Cu–Sn intermetallic compound (IMC) at the tin-based solder/Cu interface during solder reaction, the reliability of this type of solder joint is a serious concern. In this work, electroless nickel–phosphorous (Ni–P) layer was deposited on the Cu pad of the flexible substrate as a diffusion barrier between Cu and the solder materials. The deposition was carried out in a commercial acidic sodium hypophosphite bath at 85 °C for different pH values. It was found that for the same deposition time period, higher pH bath composition (mild acidic) yields thicker Ni–P layer with lower phosphorous content. Solder balls having composition 62%Sn–36%Pb–2%Ag were reflowed at 240 °C for 1 to 180 min on three types of electroless Ni–P layers deposited at the pH value of 4, 4.8 and 6, respectively. Thermal stability of the electroless Ni–P barrier layer against the Sn–36%Pb–2%Ag solder reflowed for different time periods was examined by scanning electron microscopy equipped with energy dispersed X-ray. Solder ball shear test was performed in order to find out the relationship between the mechanical strength of solder joints and the characteristics of the electroless Ni–P layer deposited. The layer deposited in the pH 4 acidic bath showed the weak barrier against reflow soldering whereas layer deposited in pH 6 acidic bath showed better barrier against reflow soldering. Mechanical strength of the joints were deteriorated quickly in the layer deposited at pH 4 acidic bath, which was found to be thin and has a high phosphorous content. From the cross-sectional studies and fracture surface analyses, it was found that the appearance of the dark crystalline phosphorous-rich Ni layer weakened the interface and hence lower solder ball shear strength. Ni–Sn IMC formed at the interfaces was found to be more stable at the low phosphorous content (∼14 at.%) layer. Electroless Ni–P deposited at mild acidic bath resulting phosphorous content of around 14 at.% is suggested as the best barrier layer for Sn–36%Pb–2%Ag solder.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

The UK 9/11 evacuation study: Analysis of survivors’ recognition and response phase in WTC1

The September 11th 2001 impact on the World Trade Centre (WTC) resulted in one of the most significant evacuations of a high-rise building in modern times. The UK High-rise Evacuation Evaluation Database (HEED) study aimed to capture and collate the experiences and behaviours of WTC evacuees in a database, which would facilitate and encourage future research, which in turn would influence the design construction and use of safer built environments. A data elicitation tool designed for the purpose comprised a pre-interview questionnaire followed by a one-to-one interview protocol consisting of free-flow narratives and semi-structured interviews of WTC evacuees. This paper, which is one in a series dealing with issues relating to the successful evacuations of towers 1 and 2, focuses on cue recognition and response patterns within WTC1. Results are presented by vertical floor clusters and include information regarding cues experienced, activities prior and subsequent to occupants first becoming aware that something was wrong, perceived personal risk, time taken to respond and the inter-relationships between them. The results indicate differences in occupant activities across the floor clusters and suggest that these differences can be explained in terms of the perception of risk and the nature and extent of cues received by the participants.