Modelling of arc welding : the importance of including the arc plasma in the computational domain

We present results of computational simulations of tungsten-inert-gas and metal-inert-gas welding. The arc plasma and the electrodes (including the molten weld pool when necessary) are included self-consistently in the computational domain. It is shown, using three examples, that it would be impossible to accurately estimate the boundary conditions on the weld-pool surface without including the arc plasma in the computational domain. First, we show that the shielding gas composition strongly affects the properties of the arc that influence the weld pool: heat flux density, current density, shear stress and arc pressure at the weld-pool surface. Demixing is found to be important in some cases. Second, the vaporization of the weld-pool metal and the diffusion of the metal vapour into the arc plasma are found to decrease the heat flux density and current density to the weld pool. Finally, we show that the shape of the wire electrode in metal-inert-gas welding has a strong influence on flow velocities in the arc and the pressure and shear stress at the weld-pool surface. In each case, we present evidence that the geometry and depth of the weld pool depend strongly on the properties of the arc.

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.

User behaviour modelling in a multi-dimensional environment for personalization and recommendation

Handling information overload online, from the user's point of view is a big challenge, especially when the number of websites is growing rapidly due to growth in e-commerce and other related activities. Personalization based on user needs is the key to solving the problem of information overload. Personalization methods help in identifying relevant information, which may be liked by a user. User profile and object profile are the important elements of a personalization system. When creating user and object profiles, most of the existing methods adopt two-dimensional similarity methods based on vector or matrix models in order to find inter-user and inter-object similarity. Moreover, for recommending similar objects to users, personalization systems use the users-users, items-items and users-items similarity measures. In most cases similarity measures such as Euclidian, Manhattan, cosine and many others based on vector or matrix methods are used to find the similarities. Web logs are high-dimensional datasets, consisting of multiple users, multiple searches with many attributes to each. Two-dimensional data analysis methods may often overlook latent relationships that may exist between users and items. In contrast to other studies, this thesis utilises tensors, the high-dimensional data models, to build user and object profiles and to find the inter-relationships between users-users and users-items. To create an improved personalized Web system, this thesis proposes to build three types of profiles: individual user, group users and object profiles utilising decomposition factors of tensor data models. A hybrid recommendation approach utilising group profiles (forming the basis of a collaborative filtering method) and object profiles (forming the basis of a content-based method) in conjunction with individual user profiles (forming the basis of a model based approach) is proposed for making effective recommendations. A tensor-based clustering method is proposed that utilises the outcomes of popular tensor decomposition techniques such as PARAFAC, Tucker and HOSVD to group similar instances. An individual user profile, showing the user's highest interest, is represented by the top dimension values, extracted from the component matrix obtained after tensor decomposition. A group profile, showing similar users and their highest interest, is built by clustering similar users based on tensor decomposed values. A group profile is represented by the top association rules (containing various unique object combinations) that are derived from the searches made by the users of the cluster. An object profile is created to represent similar objects clustered on the basis of their similarity of features. Depending on the category of a user (known, anonymous or frequent visitor to the website), any of the profiles or their combinations is used for making personalized recommendations. A ranking algorithm is also proposed that utilizes the personalized information to order and rank the recommendations. The proposed methodology is evaluated on data collected from a real life car website. Empirical analysis confirms the effectiveness of recommendations made by the proposed approach over other collaborative filtering and content-based recommendation approaches based on two-dimensional data analysis methods.

Computational approaches to the visual validation of 3D virtual environments

Virtual environments can provide, through digital games and online social interfaces, extremely exciting forms of interactive entertainment. Because of their capability in displaying and manipulating information in natural and intuitive ways, such environments have found extensive applications in decision support, education and training in the health and science domains amongst others. Currently, the burden of validating both the interactive functionality and visual consistency of a virtual environment content is entirely carried out by developers and play-testers. While considerable research has been conducted in assisting the design of virtual world content and mechanics, to date, only limited contributions have been made regarding the automatic testing of the underpinning graphics software and hardware. The aim of this thesis is to determine whether the correctness of the images generated by a virtual environment can be quantitatively defined, and automatically measured, in order to facilitate the validation of the content. In an attempt to provide an environment-independent definition of visual consistency, a number of classification approaches were developed. First, a novel model-based object description was proposed in order to enable reasoning about the color and geometry change of virtual entities during a play-session. From such an analysis, two view-based connectionist approaches were developed to map from geometry and color spaces to a single, environment-independent, geometric transformation space; we used such a mapping to predict the correct visualization of the scene. Finally, an appearance-based aliasing detector was developed to show how incorrectness too, can be quantified for debugging purposes. Since computer games heavily rely on the use of highly complex and interactive virtual worlds, they provide an excellent test bed against which to develop, calibrate and validate our techniques. Experiments were conducted on a game engine and other virtual worlds prototypes to determine the applicability and effectiveness of our algorithms. The results show that quantifying visual correctness in virtual scenes is a feasible enterprise, and that effective automatic bug detection can be performed through the techniques we have developed. We expect these techniques to find application in large 3D games and virtual world studios that require a scalable solution to testing their virtual world software and digital content.

Mechanical testing and modelling of a bone-implant construct

Finite Element modelling of bone fracture fixation systems allows computational investigation of the deformation response of the bone to load. Once validated, these models can be easily adapted to explore changes in design or configuration of a fixator. The deformation of the tissue within the fracture gap determines its healing and is often summarised as the stiffness of the construct. FE models capable of reproducing this behaviour would provide valuable insight into the healing potential of different fixation systems. Current model validation techniques lack depth in 6D load and deformation measurements. Other aspects of the FE model creation such as the definition of interfaces between components have also not been explored. This project investigated the mechanical testing and FE modelling of a bone– plate construct for the determination of stiffness. In depth 6D measurement and analysis of the generated forces, moments and movements showed large out of plane behaviours which had not previously been characterised. Stiffness calculated from the interfragmentary movement was found to be an unsuitable summary parameter as the error propagation is too large. Current FE modelling techniques were applied in compression and torsion mimicking the experimental setup. Compressive stiffness was well replicated, though torsional stiffness was not. The out of plane behaviours prevalent in the experimental work were not replicated in the model. The interfaces between the components were investigated experimentally and through modification to the FE model. Incorporation of the interface modelling techniques into the full construct models had no effect in compression but did act to reduce torsional stiffness bringing it closer to that of the experiment. The interface definitions had no effect on out of plane behaviours, which were still not replicated. Neither current nor novel FE modelling techniques were able to replicate the out of plane behaviours evident in the experimental work. New techniques for modelling loads and boundary conditions need to be developed to mimic the effects of the entire experimental system.

How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates

Currently, finite element analyses are usually done by means of commercial software tools. Accuracy of analysis and computational time are two important factors in efficiency of these tools. This paper studies the effective parameters in computational time and accuracy of finite element analyses performed by ANSYS and provides the guidelines for the users of this software whenever they us this software for study on deformation of orthopedic bone plates or study on similar cases. It is not a fundamental scientific study and only shares the findings of the authors about structural analysis by means of ANSYS workbench. It gives an idea to the readers about improving the performance of the software and avoiding the traps. The solutions provided in this paper are not the only possible solutions of the problems and in similar cases there are other solutions which are not given in this paper. The parameters of solution method, material model, geometric model, mesh configuration, number of the analysis steps, program controlled parameters and computer settings are discussed through thoroughly in this paper.

Mathematical modelling of human corneal oxygenation and cell kinetics in corneal epithelial wound healing

Healthy transparent cornea depends upon the regulation of fluid, nutrient and oxygen transport through the tissue to sustain cell metabolism and other critical processes for normal functioning. This research considers the corneal geometry and investigates oxygen distribution using a two-dimensional Monod kinetic model, showing that previous studies make assumptions that lead to predictions of near-anoxic levels of oxygen tension in the limbal regions of the cornea. It also considers the comparison of experimental spatial and temporal data with the predictions of novel mathematical models with respect to distributed mitotic rates during corneal epithelial wound healing.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.