Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

An internet of social things

The Internet of Things is a vision for a world of interconnected smart devices. We present an alternative vision based on a review of literature that emphasizes the importance and role of objects in social relations. We situate this work in relation to a conceptual understanding of objects and sociality, and note some methodological implications of a more object-centred sociality that may suggest design opportunities alongside the emerging Internet of Things.

The ways of things: Objects in the studio

Conventions of the studio presuppose the artist as the active agent, imposing his/her will upon and through objects that remain essentially inert. However, this characterisation of practice overlooks the complex object dynamics that underpin the art-making process. Far from passive entities, objects are resistant, ‘speaking back’ to the artist, impressing their will upon their surroundings. Objects stick to one another, fall over, drip, spill, spatter and chip one another. Objects support, dismantle, cover and transform one another. Objects are both the apparatus of the studio and its products. It can be argued that the work of art is as much shaped by objects as it is by human impulse. Within this alternate ontology, the artist becomes but one element in a constellation of objects. Drawing upon Graham Harman’s Object-Oriented Ontology and a selection of photographs of my studio processes, this practice-led paper will explore the notion of agentive objects and the ways in which the contemporary art studio can be reconsidered as a primary site for the production of new object relationships.

The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Making things happen: How the environment triggers action

Innovative research conducted by Dr Jan Golembiewski from Medical Architectures Australasia-Pacific, in the area of environmental design for mental healthcare helps us reflect, through experiential storytelling, on the importance of paying attention to positive environmental ‘triggers for action’ when designing physical spaces to help manage particular patients’ conditions. This article is written about the mental health experience specifically, however environmental design is an issue we can all relate to in our everyday lives (at home, at work, social spots or in places such as hospitals or retreats) when we instinctively notice a connection between our mental health and our surroundings or a healthy sense of place.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Interaction design for tablet based edutainment systems for mathematical education of primary student

Mathematics has been perceived as the core area of learning in most educational systems around the world including Sri Lanka. Unfortunately, it is clearly visible that a majority of Sri Lankan students are failing in their basic mathematics when the recent grade five scholarship examination and ordinary level exam marks are analysed. According to Department of Examinations Sri Lanka , on average, over 88 percent of the students are failing in the grade 5 scholarship examinations where mathematics plays a huge role while about 50 percent of the students fail in there ordinary level mathematics examination. Poor or lack of basic mathematics skills has been identified as the root cause.