Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a twodimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.

Kappa calculus and evidential strength: A note on Åqvist's logical theory of legal evidence

Lennart Åqvist (1992) proposed a logical theory of legal evidence, based on the Bolding-Ekelöf of degrees of evidential strength. This paper reformulates Åqvist's model in terms of the probabilistic version of the kappa calculus. Proving its acceptability in the legal context is beyond the present scope, but the epistemological debate about Bayesian Law isclearly relevant. While the present model is a possible link to that lineof inquiry, we offer some considerations about the broader picture of thepotential of AI & Law in the evidentiary context. Whereas probabilisticreasoning is well-researched in AI, calculations about the threshold ofpersuasion in litigation, whatever their value, are just the tip of theiceberg. The bulk of the modeling desiderata is arguably elsewhere, if one isto ideally make the most of AI's distinctive contribution as envisaged forlegal evidence research.

[Book review] Theory of Games and Economic Behaviour

Tony Mann provides a review of the book: Theory of Games and Economic Behavior, John von Neumann and Oskar Morgenstern, Princeton University Press, 1944.

[Book review] Collaborative learning in mathematics

Review of: Collaborative Learning in Mathematics: A challenge to our beliefs and practices by Malcolm Swan, National Institute of Adult Continuing Education, paperback £24.95, ISBN 981-1-86201-311-7; hardback £44.95, ISBN 978-1-86201-316-2.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Can density functional theory (DFT) be used as an aid to a deeper understanding of tandem mass spectrometric fragmentation pathways?

Prediction of tandem mass spectrometric (MS/MS) fragmentation for non-peptidic molecules based on structure is of immense interest to the mass spectrometrist. If a reliable approach to MS/MS prediction could be achieved its impact within the pharmaceutical industry could be immense. Many publications have stressed that the fragmentation of a molecular ion or protonated molecule is a complex process that depends on many parameters, making prediction difficult. Commercial prediction software relies on a collection of general heuristic rules of fragmentation, which involve cleaving every bond in the structure to produce a list of 'expected' masses which can be compared with the experimental data. These approaches do not take into account the thermodynamic or molecular orbital effects that impact on the molecule at the point of protonation which could influence the potential sites of bond cleavage based on the structural motif. A series of compounds have been studied by examining the experimentally derived high-resolution MS/MS data and comparing it with the in silico modelling of the neutral and protonated structures. The effect that protonation at specific sites can have on the bond lengths has also been determined. We have calculated the thermodynamically most stable protonated species and have observed how that information can help predict the cleavage site for that ion. The data have shown that this use of in silico techniques could be a possible way to predict MS/MS spectra. Copyright (C) 2009 John Wiley & Sons, Ltd.

Policy packages as potential routes to urban road pricing in the UK

This paper focuses on urban road pricing as a demand management policy that is often regarded as radical and generally unacceptable. Road pricing often gets delayed or abandoned due to low acceptability. This may be due to the fact that complex interactions and drivers of change affect road transport management and require cooperation within implementation networks. The implementation network is a group of people (referred to as partners and actors) who co-ordinate the introduction of policy tools. The drivers of change include any internal or external influences that have an effect on the time, place, or ‘shape’ of the policy measures being introduced. Demand management measures that focus on 'sustainable transport' usually address a limited set of objectives and are often implemented alone i.e. are not necessarily combined with other policy measures. When combined with other measures, it is not always clear whether the multiple interactions between policy tools and implementation networks have been sufficiently considered. Examples of ongoing implementation of policy package in the UK are the support of road pricing initiatives combined with public transport improvements by the Transport Innovation Fund. The objectives of the paper are twofold. First, we present a review of the UK urban road pricing situation. Second, we contrast the emerging issues against six key implementation factors. The analysis of three existing UK road pricing examples - London, Edinburgh and Durham – shows the importance of combining policy tools. Furthermore, through the above examples and theoretical arguments, we emphasise the additional need of creating and maintaining strong networks when implementing policy packages.

Student nurses need more than maths to improve their drug calculating skills

Nurses need to be able to calculate accurate drug calculations in order to safely administer drugs to their patients (NMC, 2002). Studies have shown however that nurses do not always have the necessary skills to calculate accurate drug dosages and are potentially administering incorrect dosages of drugs to their patients (Hutton, M. 1998. Nursing Mathematics: the importance of application. Nursing Standard 13(11), 35–38; Kapborg, I. 1994. Calculation and administration of drug dosage by Swedish nurses, Student Nurses and Physicians. International Journal for Quality in Health Care 6(4), 389–395; O’Shea, E. 1999. Factors contributing to medication errors: a literature review. Journal of Advanced Nursing 8, 496–504; Wilson, A. 2003. Nurses maths: researching a practical approach. Nursing Standard 17(47), 33–36). The literature indicates that in order to improve drug calculations strategies need to focus on both the mathematical skills and conceptual skills of student nurses so they can interpret clinical data into drug calculations to be solved. A study was undertaken to investigate the effectiveness of implementing several strategies which focussed on developing the mathematical and conceptual skills of student nurses to improve their drug calculation skills. The study found that implementing a range of strategies which addressed these two developmental areas significantly improved the drug calculation skills of nurses. The study also indicates that a range of strategies has the potential ensuring that the skills taught are retained by the student nurses. Although the strategies significantly improved the drug calculation skills of student nurses, the fact that only 2 students were able to achieve 100% in their drug calculation test indicates a need for further research into this area.