Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

A framework for integrating disadvantaged analysis into transportation planning models

This research paper aims to develop a method to explore the travel behaviour differences between disadvantaged and non-disadvantaged populations. It also aims to develop a modelling approach or a framework to integrate disadvantage analysis into transportation planning models (TPMs). The methodology employed identifies significantly disadvantaged groups through a cluster analysis and the paper presents a disadvantage-integrated TPM. This model could be useful in determining areas with concentrated disadvantaged population and also developing and formulating relevant disadvantage sensitive policies. (a) For the covering entry of this conference, please see ITRD abstract no. E214666.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Developing a predictive contractor satisfaction model (CoSMo) for construction projects

Over the last few decades, construction project performance has been evaluated due to the increase of delays, cost overruns and quality failures. Growing numbers of disputes, inharmonious working environments, conflict, blame cultures, and mismatches of objectives among project teams have been found to be contributory factors to poor project performance. Performance measurement (PM) approaches have been developed to overcome these issues, however, the comprehensiveness of PM as an overall approach is still criticised in terms of the iron triangle; namely time, cost, and quality. PM has primarily focused on objective measures, however, continuous improvement requires the inclusion of subjective measures, particularly contractor satisfaction (Co-S). It is challenging to deal with the two different groups of large and small-medium contractor satisfaction as to date, Co-S has not been extensively defined, primarily in developing countries such as Malaysia. Therefore, a Co-S model is developed in this research which aims to fulfil the current needs in the construction industry by integrating performance measures to address large and small-medium contractor perceptions. The positivist paradigm used in the research was adhered to by reviewing relevant literature and evaluating expert discussions on the research topic. It yielded a basis for the contractor satisfaction model (CoSMo) development which consists of three elements: contractor satisfaction (Co-S) dimensions; contributory factors and characteristics (project and participant). Using valid questionnaire results from 136 contractors in Malaysia lead to the prediction of several key factors of contractor satisfaction and to an examination of the relationships between elements. The relationships were examined through a series of sequential statistical analyses, namely correlation, one-way analysis of variance (ANOVA), t-tests and multiple regression analysis (MRA). Forward and backward MRAs were used to develop Co-S mathematical models. Sixteen Co-S models were developed for both large and small-medium contractors. These determined that the large contractor Malaysian Co-S was most affected by the conciseness of project scope and quality of the project brief. Contrastingly, Co-S for small-medium contractors was strongly affected by the efficiency of risk control in a project. The results of the research provide empirical evidence in support of the notion that appropriate communication systems in projects negatively contributes to large Co-S with respect to cost and profitability. The uniqueness of several Co-S predictors was also identified through a series of analyses on small-medium contractors. These contractors appear to be less satisfied than large contractors when participants lack effectiveness in timely authoritative decision-making and communication between project team members. Interestingly, the empirical results show that effective project health and safety measures are influencing factors in satisfying both large and small-medium contractors. The perspectives of large and small-medium contractors in respect to the performance of the entire project development were derived from the Co-S models. These were statistically validated and refined before a new Co-S model was developed. Developing such a unique model has the potential to increase project value and benefit all project participants. It is important to improve participant collaboration as it leads to better project performance. This study may encourage key project participants; such as client, consultant, subcontractor and supplier; to increase their attention to contractor needs in the development of a project. Recommendations for future research include investigating other participants‟ perspectives on CoSMo and the impact of the implementation of CoSMo in a project, since this study is focused purely on the contractor perspective.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Contextual models and the non-Newtonian paradigm

Biological systems exhibit a wide range of contextual effects, and this often makes it difficult to construct valid mathematical models of their behaviour. In particular, mathematical paradigms built upon the successes of Newtonian physics make assumptions about the nature of biological systems that are unlikely to hold true. After discussing two of the key assumptions underlying the Newtonian paradigm, we discuss two key aspects of the formalism that extended it, Quantum Theory (QT). We draw attention to the similarities between biological and quantum systems, motivating the development of a similar formalism that can be applied to the modelling of biological processes.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

A systematic approach for selecting lean strategies and assessing leanness in manufacturing organizations

Lean strategies have been developed to eliminate or reduce manufacturing waste and thus improve operational efficiency in manufacturing processes. However, implementing lean strategies requires a large amount of resources and, in practice, manufacturers encounter difficulties in selecting appropriate lean strategies within their resource constraints. There is currently no systematic methodology available for selecting appropriate lean strategies within a manufacturer's resource constraints. In the lean transformation process, it is also critical to measure the current and desired leanness levels in order to clearly evaluate lean implementation efforts. Despite the fact that many lean strategies are utilized to reduce or eliminate manufacturing waste, little effort has been directed towards properly assessing the leanness of manufacturing organizations. In practice, a single or specific group of metrics (either qualitative or quantitative) will only partially measure the overall leanness. Existing leanness assessment methodologies do not offer a comprehensive evaluation method, integrating both quantitative and qualitative lean measures into a single quantitative value for measuring the overall leanness of an organization. This research aims to develop mathematical models and a systematic methodology for selecting appropriate lean strategies and evaluating the leanness levels in manufacturing organizations. Mathematical models were formulated and a methodology was developed for selecting appropriate lean strategies within manufacturers' limited amount of available resources to reduce their identified wastes. A leanness assessment model was developed by using the fuzzy concept to assess the leanness level and to recommend an optimum leanness value for a manufacturing organization. In the proposed leanness assessment model, both quantitative and qualitative input factors have been taken into account. Based on program developed in MATLAB and C#, a decision support tool (DST) was developed for decision makers to select lean strategies and evaluate the leanness value based on the proposed models and methodology hence sustain the lean implementation efforts. A case study was conducted to demonstrate the effectiveness of these proposed models and methodology. Case study results suggested that out of 10 wastes identified, the case organization (ABC Limited) is able to improve a maximum of six wastes from the selected workstation within their resource limitations. The selected wastes are: unnecessary motion, setup time, unnecessary transportation, inappropriate processing, work in process and raw material inventory and suggested lean strategies are: 5S, Just-In-Time, Kanban System, the Visual Management System (VMS), Cellular Manufacturing, Standard Work Process using method-time measurement (MTM), and Single Minute Exchange of Die (SMED). From the suggested lean strategies, the impact of 5S was demonstrated by measuring the leanness level of two different situations in ABC. After that, MTM was suggested as a standard work process for further improvement of the current leanness value. The initial status of the organization showed a leanness value of 0.12. By applying 5S, the leanness level significantly improved to reach 0.19 and the simulation of MTM as a standard work method shows the leanness value could be improved to 0.31. The optimum leanness value of ABC was calculated to be 0.64. These leanness values provided a quantitative indication of the impacts of improvement initiatives in terms of the overall leanness level to the case organization. Sensitivity analsysis and a t-test were also performed to validate the model proposed. This research advances the current knowledge base by developing mathematical models and methodologies to overcome lean strategy selection and leanness assessment problems. By selecting appropriate lean strategies, a manufacturer can better prioritize implementation efforts and resources to maximize the benefits of implementing lean strategies in their organization. The leanness index is used to evaluate an organization's current (before lean implementation) leanness state against the state after lean implementation and to establish benchmarking (the optimum leanness state). Hence, this research provides a continuous improvement tool for a lean manufacturing organization.

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.

Models of survivorship care provision in adult patients with haematological cancer : an integrative literature review

Purpose: Increasing numbers of haematology cancer survivors warrants identification of the most effective model of survivorship care to survivors from a diverse range of haematological cancers with aggressive treatment regimens. This review aimed to identify models of survivorship care to support the needs of haematology cancer survivors. Methods: An integrative literature review method utilised a search of electronic databases (CINAHL, Medline, PsycInfo, PubMed, EMBASE, PsycArticles, Cochrane Library) for eligible articles (up to July 2014). Articles were included if they proposed or reported the use of a model of care for haematology cancer survivors. Results: Fourteen articles were included in this review. Eight articles proposed and described models of care and six reported the use of a range of survivorship models of care in haematology cancer survivors. No randomised controlled trials or literature reviews were found to have been undertaken specifically with this cohort of cancer survivors. There was variation in the models described and who provided the survivorship care. Conclusion: Due to the lack of studies evaluating the effectiveness of models of care, it is difficult to determine the best model of care for haematology cancer survivors. Many different models of care are being put into practice before robust research is conducted. Therefore well-designed high quality pragmatic randomised controlled trials are required to inform clinical practice.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.