Wear mechanisms and scale effects in two-body abrasion

The ‘particle size effect’ and its manifestation in abrasion still attracts considerable debate as to its origins and the ranking of its likely causes. Experiments have been conducted to study the important contribution that the formation of wear debris can have on the progression of wear. The experiments consist of unlubricated (dry) pin-on-disk tests with silicon carbide coated paper of varying particle size, with different pin material, diameter and loads. It has been observed that the influence of debris formation on wear rate is more pronounced for fine abrasives and soft-wearing materials. Consequently, it is proposed that the particle size effect can be explained in terms of geometrical scaling and the evolution of third-body effects with diminishing particle diameter.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Numerical study of two ill-posed one-phase Stefan problems

We treat two related moving boundary problems. The first is the ill-posed Stefan problem for melting a superheated solid in one Cartesian coordinate. Mathematically, this is the same problem as that for freezing a supercooled liquid, with applications to crystal growth. By applying a front-fixing technique with finite differences, we reproduce existing numerical results in the literature, concentrating on solutions that break down in finite time. This sort of finite-time blow-up is characterised by the speed of the moving boundary becoming unbounded in the blow-up limit. The second problem, which is an extension of the first, is proposed to simulate aspects of a particular two-phase Stefan problem with surface tension. We study this novel moving boundary problem numerically, and provide results that support the hypothesis that it exhibits a similar type of finite-time blow-up as the more complicated two-phase problem. The results are unusual in the sense that it appears the addition of surface tension transforms a well-posed problem into an ill-posed one.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Effective attacking strategies in rugby union

Evasive change-of-direction manoeuvres (agility skills) are a fundamental ability in rugby union. In this study, we explored the attributes of agility skill execution as they relate to effective attacking strategies in rugby union. Seven Super 14 games were coded using variables that assessed team patterns and individual movement characteristics during attacking ball carries. The results indicated that tackle-breaks are a key determinant of try-scoring ability and team success in rugby union. The ability of the attacking ball carrier to receive the ball at high speed with at least two body lengths from the defence line against an isolated defender promoted tackle-breaks. Furthermore, the execution of a side-step evasive manoeuvre at a change of direction angle of 20–60° and a distance of one to two body lengths from the defence, and then straightening the running line following the initial direction change at an angle of 20–60°, was associated with tackle-breaks. This study provides critical insight regarding the attributes of agility skill execution that are associated with effective ball carries in rugby union.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Efficiency of parallelisation of genetic algorithms in the data analysis context

Most real-life data analysis problems are difficult to solve using exact methods, due to the size of the datasets and the nature of the underlying mechanisms of the system under investigation. As datasets grow even larger, finding the balance between the quality of the approximation and the computing time of the heuristic becomes non-trivial. One solution is to consider parallel methods, and to use the increased computational power to perform a deeper exploration of the solution space in a similar time. It is, however, difficult to estimate a priori whether parallelisation will provide the expected improvement. In this paper we consider a well-known method, genetic algorithms, and evaluate on two distinct problem types the behaviour of the classic and parallel implementations.

Two voices : the marginalised body as a voice & Imperfect Offerings a novel

This thesis investigates the phenomenon of self-harm as a form of political protest using two different, but complementary, methods of inquiry: a theoretical research project and a novel. Through these two approaches, to the same research problem, I examine how we can re-position the body that self-harms in political protest from weapon to voice; and in doing so find a path towards ethical and equitable dialogue between marginalised and mainstream communities. The theoretical, or academic, portion of the thesis examines self-harm as protest, positing these acts as a form of tactical selfharm, and acknowledge its emergence as a voice for the otherwise silenced in the public sphere. Through the use of phenomenology and feminist theory I examine the body as site for political agency, the circumstances which surround the use of the body for protest, and the reaction to tactical self-harm by the individual and the state. Using Bakhtin’s concept of dialogism, and the dialogic space I propose that by ‘hearing’ the body engaged in tactical selfharm we come closer to entering into an ethical dialogue with the otherwise silenced in our communities (locally, nationally and globally). The novel, Imperfect Offerings, explores these ideas in a fictional world, and allows me to put faces, names and lives to those who are compelled to harm their bodies to be heard. Also using Bakhtin’s framework I encourage a dialogue between the critical and creative parts of the thesis, challenging the traditional paradigm of creative PhD projects as creative work and exegesis.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

Problem-solving courts, therapeutic jurisprudence and the constitution : if two is company, is three a crowd?

Court costs, resource-intensive trials, booming prison populations and the obduracy of recidivism rates all present as ugly excesses of the criminal law adversarial paradigm. To combat these excesses, problem-solving courts have evolved with an edict to address the underlying issues that have caused an individual to commit a crime. When a judge seeks to help a problem-solving court participant deal with issues like addiction, mental health or poverty, they are performing a very different role to that of a judicial officer in the traditional court hierarchy. They are no longer the removed, independent arbiter — a problem-solving court judge steps into the ‘arena’ with the participant and makes active use of their judicial authority to assist in rehabilitation and positive behavioural change. Problem-solving court judges employing the principles of therapeutic jurisprudence appreciate that their interaction with participants can have therapeutic and anti-therapeutic consequences. This article will consider how the deployment of therapeutic measures (albeit with good intention) can lead to the behavioural manifestation of partiality and bias on the part of problem-solving court judges. Chapter III of the Commonwealth Constitution will then be analysed to highlight why the operation and functioning of problem solving courts may be deemed unconstitutional. Part IV of this article will explain how a problem-solving court judge who is not acting impartially or independently will potentially contravene the requirements of the Constitution. It will finally be suggested that judges who possess a high level of emotional intelligence will be the most successful in administering an independent and impartial problem solving court.

Assessing the impact of a food supplement on the nutritional status and body composition of HIV-infected Zambian women on ARVs

Background Zambia is a sub-Saharan country with one of the highest prevalence rates of HIV, currently estimated at 14%. Poor nutritional status due to both protein-energy and micronutrient malnutrition has worsened this situation. In an attempt to address this combined problem, the government has instigated a number of strategies, including the provision of antiretroviral (ARV) treatment coupled with the promotion of good nutrition. High-energy protein supplement (HEPS) is particularly promoted; however, the impact of this food supplement on the nutritional status of people living with HIV/AIDS (PLHA) beyond weight gain has not been assessed. Techniques for the assessment of nutritional status utilising objective measures of body composition are not commonly available in Zambia. The aim of this study is therefore to assess the impact of a food supplement on nutritional status using a comprehensive anthropometric protocol including measures of skinfold thickness and circumferences, plus the criterion deuterium dilution technique to assess total body water (TBW) and derive fat-free mass (FFM) and fat mass (FM). Methods/Design This community-based controlled and longitudinal study aims to recruit 200 HIV-infected females commencing ARV treatment at two clinics in Lusaka, Zambia. Data will be collected at four time points: baseline, 4-month, 8-month and 12-month follow-up visits. Outcome measures to be assessed include body height and weight, body mass index (BMI), body composition, CD4, viral load and micronutrient status. Discussion This protocol describes a study that will provide a longitudinal assessment of the impact of a food supplement on the nutritional status of HIV-infected females initiating ARVs using a range of anthropometric and body composition assessment techniques.