Recent Submissions

  • The early stages of biofilm formation by Staphylococcus epidermidis studied by XPS and AFM

    Smith, Graham; Bava, Radhika (University of Chester, 2019-09)
    Staphylococcus epidermidis is an opportunistic bacteria which forms pathogenic biofilms in medical implant environment. Biofilm formation is a complex multistage process within which the initial stages of adhesion are deemed the most critical target for preventing biofilms. This research involves the characterisation of S. epidermidis (ATCC35984 and NCTC13360) by using X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM) on model substrates including glass, muscovite mica, silicon (111) wafer, sputter-coated titanium and sputter-coated silver, focusing on the effect of chemical properties of the material on adhesion by using surfaces with minimal roughness. AFM was used to image the surface, from which bacterial coverage can be estimated. AFM was also used to probe adhesion forces and local mechanical properties of all samples through the use of force-distance curves. AFM images were also used to estimate the bacterial coverage. XPS was used to investigate the surface chemistry from the layer thicknesses, the percentage coverage and potential composition of the overlayer. The combination of these techniques allow the relationships between the surface chemistry of the substrate and the bacteria to be correlated with changes in coverage and properties of bacterial films. Data on incubated bacterial samples were compared with those from the reference substrates, both before and after autoclaving, and from samples prepared using protein rich growth medium (tryptic soy broth) in the absence of bacteria as well as a pure bacterial pellet in an assumed non-biofilm forming state. The research indicates the potential differences between biofilm and non-biofilm former strains, with both strains being covered by an organic layer with little influence of the growth media used to incubate the bacteria. This research also shows how XPS and AFM data can be combined and applied to bacterial adhesion.
  • Factors for successful Agile collaboration between UX designers and software developers in a complex organisation

    Avis, Nick; Kerins, John; Jones, Alexander J (University of Chester, 2019-07-23)
    User Centred Design (UCD) and Agile Software Development (ASD) processes have been two extremely successful methods for software development in recent years. However, both have been repeatedly described as frequently putting contradictory demands on people working with the respective processes. The current research addresses this point by focussing on the crucial relationship between a User Experience (UX) designer and a software developer. In-depth interviews, an online survey, a contextual inquiry and a diary study are described from a sample of over 100 designers, developers and their stakeholders (managers) in a large media organisation exploring factors for success in Agile development cycles. The findings from the survey show that organisational separation is challenge for agile collaboration between the two roles and while designers and developers have similar levels of (moderately positive) satisfaction with Agile processes, there are differences between the two roles. While developers are happier with the wider teamwork but want more access to and close collaboration with designers, particularly in an environment set up for Agile practices, the designers’ concern was the quality of the wider teamwork. The respondent’s comments also identified that the two roles saw a close – and ideally co-located – cooperation as essential for improving communication, reducing inefficiencies, and avoiding bad products being released. These results reflected the findings from the in-depth interviews with stakeholders. In particular, it was perceived that co-located pairing helped understanding different role-dependent demands and skills, increased efficiency of prototyping and implementing changes, and enabling localised decision-making. However, organisational processes, the setup of work-environment, and managerial traditions meant that this close collaboration and localised decision-making was often not possible to maintain over extended periods. Despite this, the studies conducted between pairs of designers and developers, found that successful collaboration between designers and developers can be found in a complex organisational setting. From the analysis of the empirical studies, six contributing factors emerged that support this. These factors are 1) Close proximity, 2) Early and frequent communication, 3) Shared ideation and problem solving, 4) Crossover of knowledge and skills, 5) Co-creation and prototyping and 6) Making joint decisions. These factors are crucially determined and empowered by the support from the organisational setting and 3 teams where practitioners work. Specifically, by overcoming key challenges to enable integration between UCD and ASD and thus encouraging close collaboration between UX designers and software developers, these challenges are: 1) Organisational structure and team culture, 2) Location and environmental setup and 3) Decision-making. These challenges along with the six factors that enable successful Agile collaboration between designers and developers provide the main contributions of this research. These contributions can be applied within large complex organisations by adopting the suggested ‘Paired Collaboration Manifesto’ to improve the integration between UCD and ASD. Beyond this, more empirical studies can take place, further extending improvements to the collaborative practices between the design and development roles and their surrounding teams.
  • Using Mathematical Modelling and Electrochemical Analysis to Investigate Age‐Associated Disease

    McAuley, Mark; Morgan, Amy (University of Chester, 2019-04-02)
    People are living longer. With this rise in life expectancy, a concomitant rise in morbidity in later life is observed; with conditions including cardiovascular disease (CVD), and cancer. However, ageing and the pathogenesis of age related disease, can be difficult to study, as the ageing process is a complex process, which affects multiple systems and mechanisms. The aim of this research was two‐fold. The first aim was to use mathematical modelling to investigate the mechanisms underpinning cholesterol metabolism, as aberrations to this system are associated with an increased risk for CVD. To better understand cholesterol from a mechanistic perspective, a curated kinetic model of whole body cholesterol metabolism, from the BioModels database, was expanded in COPASI, to produce a model with a broader range of mechanisms which underpin cholesterol metabolism. A range of time course data, and local and global parameter scans were utilised to examine the effect of cholesterol feeding, saturated fat feeding, ageing, and cholesterol ester transfer protein (CETP) genotype. These investigations revealed: the model behaved as a hypo‐responder to cholesterol feeding, the robustness of the cholesterol biosynthesis pathway, and the impact CETP can have on healthy ageing. The second aim of this work was to use electrochemical techniques to detect DNA methylation within the engrailed homeobox 1 (EN1) gene promoter, which has been implicated in cancer. Hypermethylation of this gene promoter is often observed in a diseased state. Synthetic DNA, designed to represent methylated and unmethylated variants, were adsorbed onto a gold rotating disk electrode for electrochemical analysis by 1) electrochemical impedance spectroscopy (EIS), 2) cyclic voltammetry (CV) and 3) differential pulse voltammetry (DPV). The technique was then applied to bisulphite modified and asymmetrically amplified DNA from the breast cancer cell line MCF‐7. Results indicated that electrochemical techniques could detect DNA methylation in both synthetic and cancer derived DNA, with EIS producing superiorresults. These non‐traditional techniques ofstudying age related disease were effective for the investigation of cholesterol metabolism and DNA methylation, and this work highlights how these techniques could be used to elucidate mechanisms or diagnose/monitor disease pathogenesis, to reduce morbidity in older people
  • Virtual and Mixed Reality Support for Activities of Daily Living

    John, Nigel; Day, Thomas W. (University of Chester, 2019-05-14)
    Rehabilitation and training are extremely important process that help people who have suffered some form of trauma to regain their ability to live independently and successfully complete activities of daily living. VR and MR have been used in rehabilitation and training, with examples in a range of areas such as physical and cognitive rehabilitation, and medical training. However, previous research has mainly used non-immersive VR such as using video games on a computer monitor or television. Immersive VR Head-Mounted Displays were first developed in 1965 but the devices were usually large, bulky and expensive. In 2016, the release of low-cost VR HMDs allowed for wider adoption of VR technology. This thesis investigates the impact of these devices in supporting activities of daily living through three novel applications: training driving skills for a powered wheelchair in both VR and MR; and using VR to help with the cognitive rehabilitation of stroke patients. Results from the acceptability study for VR in cognitive rehabilitation showed that patients would be likely to accept VR as a method of rehabilitation. However, factors such as visual issues need to be taken into consideration. The validation study for the Wheelchair-VR project showed promising results in terms of user improvement after the VR training session but the majority of the users experienced symptoms of cybersickness. Wheelchair-MR didn’t show statistically significant results in terms of improvements but did show a mean average improvement compared to the control group. The effects of cybersickness were also greatly reduced compared to VR. We conclude that VR and MR can be used in conjunction with modern games engines to develop virtual environments that can be adapted to accelerate the rehabilitation and training of patients coping with different aspects of daily life.
  • Investigation of size, concentration and particle shapes in hydraulic systems using an in-line CMOS image matrix sensor

    McMillan, Alison; Kornilin, Dmitriy V. (University of ChesterWrexham Glyndŵr UniversityUniversity of Chester, 2018-09-21)
    The theoretical and experimental investigation of the novel in-line CMOS image sensor was performed. This sensor is aimed to investigate particle size distribution, particle concentration and shape in hydraulic liquid in order to implement the proactive maintenance of hydraulic equipment. The existing instruments such as automatic particle counters and techniques are not sufficiently enough to address this task because of their restricted sensitivity, limit of concentration to be measured and they cannot determine particle shape. Other instruments cannot be used as inline sensors because they are not resistant to the arduous conditions such as high pressure and vibration. The novel mathematical model was proposed as it is not possible to use previously developed techniques based on using optical system and complicated algorithms. This model gives the output signal of the image sensor depending on the particle size, its distance from the light source (LED) and image sensor. Additionally, the model takes into account the limited exposure time and particle track simulation. The results of simulation based on the model are also performed in thesis. On the basis of the mathematical model the image processing algorithms were suggested in order to determine particle size even when this size is lower than pixel size. There are different approaches depending on the relation between the size of the particle and the pixel size. The approach to the volume of liquid sample estimation was suggested in order to address the problem of low accuracy of concentration measurement by the conventional automatic particle counters based on the single photodiode. Proposed technique makes corrections on the basis of particle velocity estimation. Approach to the accuracy estimation of the sensor was proposed and simulation results are shown. Generally, the accuracy of particle size and concentration measurement was considered. Ultimately, the experimental setup was used in order to test suggested techniques. The mathematical model was tested and the results showed sufficient correlation with the experiment. The zinc dust was used as a reference object as there are the particles within the range from 1 to 25 microns which is appropriate to check the sensitivity. The results of experiments using reference instrument showed the improved sensitivity and accuracy of volume measured compared to the reference one.
  • Numerical Solution of Fractional Differential Equations and their Application to Physics and Engineering

    Morgado, Luisa; Ford, Neville; Ferrás, Luís J. L. (University of Chester, 2018-12-03)
    This dissertation presents new numerical methods for the solution of fractional differential equations of single and distributed order that find application in the different fields of physics and engineering. We start by presenting the relationship between fractional derivatives and processes like anomalous diffusion, and, we then develop new numerical methods for the solution of the time-fractional diffusion equations. The first numerical method is developed for the solution of the fractional diffusion equations with Neumann boundary conditions and the diffusivity parameter depending on the space variable. The method is based on finite differences, and, we prove its convergence (convergence order of O(Δx² + Δt²<sup>-α</sup>), 0 < α < 1) and stability. We also present a brief description of the application of such boundary conditions and fractional model to real world problems (heat flux in human skin). A discussion on the common substitution of the classical derivative by a fractional derivative is also performed, using as an example the temperature equation. Numerical methods for the solution of fractional differential equations are more difficult to develop when compared to the classical integer-order case, and, this is due to potential singularities of the solution and to the nonlocal properties of the fractional differential operators that lead to numerical methods that are computationally demanding. We then study a more complex type of equations: distributed order fractional differential equations where we intend to overcome the second problem on the numerical approximation of fractional differential equations mentioned above. These equations allow the modelling of more complex anomalous diffusion processes, and can be viewed as a continuous sum of weighted fractional derivatives. Since the numerical solution of distributed order fractional differential equations based on finite differences is very time consuming, we develop a new numerical method for the solution of the distributed order fractional differential equations based on Chebyshev polynomials and present for the first time a detailed study on the convergence of the method. The third numerical method proposed in this thesis aims to overcome both problems on the numerical approximation of fractional differential equations. We start by solving the problem of potential singularities in the solution by presenting a method based on a non-polynomial approximation of the solution. We use the method of lines for the numerical approximation of the fractional diffusion equation, by proceeding in two separate steps: first, spatial derivatives are approximated using finite differences; second, the resulting system of semi-discrete ordinary differential equations in the initial value variable is integrated in time with a non-polynomial collocation method. This numerical method is further improved by considering graded meshes and an hybrid approximation of the solution by considering a non-polynomial approximation in the first sub-interval which contains the origin in time (the point where the solution may be singular) and a polynomial approximation in the remaining intervals. This way we obtain a method that allows a faster numerical solution of fractional differential equations (than the method obtained with non-polynomial approximation) and also takes into account the potential singularity of the solution. The thesis ends with the main conclusions and a discussion on the main topics presented along the text, together with a proposal of future work.
  • Controller Design Methodology for Sustainable Local Energy Systems

    Counsell, John M.; Al-khaykan, Ameer (University of Chester, 2018-11-15)
    Commercial Buildings and complexes are no longer just national heat and power network energy loads, but they are becoming part of a smarter grid by including their own dedicated local heat and power generation. They do this by utilising both heat and power networks/micro-grids. A building integrated approach of Combined Heat and Power (CHP) generation with photovoltaic power generation (PV) abbreviated as CHPV is emerging as a complementary energy supply solution to conventional (i.e. national grid based) gas and electricity grid supplies in the design of sustainable commercial buildings and communities. The merits for the building user/owner of this approach are: to reduce life time energy running costs; reduce carbon emissions to contribute to UK’s 2020/2030 climate change targets; and provide a more flexible and controllable local energy system to act as a dynamic supply and/or load to the central grid infrastructure. The energy efficiency and carbon dioxide (CO2) reductions achievable by CHP systems are well documented. The merits claimed by these solutions are predicated on the ability of these systems being able to satisfy: perfect matching of heat and power supply and demand; ability at all times to maintain high quality power supply; and to be able to operate with these constraints in a highly dynamic and unpredictable heat and power demand situation. Any circumstance resulting in failure to guarantee power quality or matching of supply and demand will result in a degradation of the achievable energy efficiency and CO2 reduction. CHP based local energy systems cannot rely on large scale diversity of demand to create a relatively easy approach to supply and demand matching (i.e. as in the case of large centralised power grid infrastructures). The diversity of demand in a local energy system is both much greater than the centralised system and is also specific to the local system. It is therefore essential that these systems have robust and high performance control systems to ensure supply and demand matching and high power quality can be achieved at all times. Ideally this same control system should be able to make best use of local energy system energy storage to enable it to be used as a flexible, highly responsive energy supply and/or demand for the centralised infrastructure. In this thesis, a comprehensive literature survey has identified that there is no scientific and rigorous method to assess the controllability or the design of control systems for these local energy systems. Thus, the main challenge of the work described in this thesis is that of a controller design method and modelling approach for CHP based local energy systems. Specifically, the main research challenge for the controller design and modelling methodology was to provide an accurate and stable system performance to deliver a reliable tracking of power drawn/supplied to the centralised infrastructure whilst tracking the require thermal comfort in the local energy systems buildings. In the thesis, the CHPV system has been used as a case study. A CHPV based solution provides all the benefits of CHP combined with the near zero carbon building/local network integrated PV power generation. CHPV needs to be designed to provide energy for the local buildings’ heating, dynamic ventilating system and air-conditioning (HVAC) facilities as well as all electrical power demands. The thesis also presents in addition to the controller design and modelling methodology a novel CHPV system design topology for robust, reliable and high-performance control of building temperatures and energy supply from the local energy system. The advanced control system solution aims to achieve desired building temperatures using thermostatic control whilst simultaneously tracking a specified national grid power demand profile. The theory is innovative as it provides a stability criterion as well as guarantees to track a specified dynamic grid connection demand profile. This research also presents: design a dynamic MATLAB simulation model for a 5-building zone commercial building to show the efficacy of the novel control strategy in terms of: delivering accurate thermal comfort and power supply; reducing the amount of CO2 emissions by the entire energy system; reducing running costs verses national rid/conventional approaches. The model was developed by inspecting the functional needs of 3 local energy system case studies which are also described in the thesis. The CHPV system is combined with supplementary gas boiler for additional heating to guarantee simultaneous tracking of all the zones thermal comfort requirements whilst simultaneously tracking a specified national grid power demand using a Photovoltaics array to supply the system with renewable energy to reduce amount of CO2 emission. The local energy system in this research can operate in any of three modes (Exporting, Importing, Island). The emphasise of the thesis modelling method has been verified to be applicable to a wide range of case studies described in the thesis chapter 3. This modelling framework is the platform for creating a generic controlled design methodology that can be applied to all these case studies and beyond, including Local Energy System (LES) in hotter climates that require a cooling network using absorption chillers. In the thesis in chapter 4 this controller design methodology using the modelling framework is applied to just one case study of Copperas Hill. Local energy systems face two types of challenges: technical and nontechnical (such as energy economics and legislation). This thesis concentrates solely on the main technical challenges of a local energy system that has been identified as a gap in knowledge in the literature survey. The gap identified is the need for a controller design methodology to allow high performance and safe integration of the local energy system with the national grid infrastructure and locally installed renewables. This integration requires the system to be able to operate at high performance and safely in all different modes of operation and manage effectively the multi-vector energy supply system (e.g. simultaneous supply of heat and power from a single system).
  • Human adipose tissue-derived mesenchymal stem/stromal cells adhere to and inhibit the growth of Staphylococcus aureus and Pseudomonas aeruginosa.

    Wood, Chelsea R.; Al Dhahri, Douaa; Al Delfi, Ibtesam; Pickles, Neil; Sammons, Rachel L.; Worthington, Tony; Wright, Karina T.; Johnson, William E. B. (2018-10-23)
    We have cultured and phenotyped human adipose tissue-derived mesenchymal stem/stromal cells (AT MSCs) and inoculated these cultures with bacteria common to infected skin wounds, i.e. Staphylococcus aureus and Pseudomonas aeruginosa. Cell interactions were examined by scanning electron microscopy (SEM), whilst bacterial growth was measured by colony forming unit (c.f.u.) and biofilm assays. AT MSCs appeared to attach to the bacteria and to engulf S. aureus. Significantly fewer bacterial c.f.u. were present in AT MSC : bacterial co-cultures compared with bacteria cultured alone. Antibacterial activity, including an inhibition of P. aeruginosa biofilm formation, was observed when bacteria were treated with conditioned medium harvested from the AT MSC :  bacterial co-cultures, irrespective of the bacterial species to which the AT MSCs had been exposed to previously. Hence, we have demonstrated that AT MSCs inhibit the growth of two common bacterial species. This was associated with bacterial adhesion, potential engulfment or phagocytosis, and the secretion of antibacterial factors.
  • Exploration and Implementation of Augmented Reality for External Beam Radiotherapy

    John, Nigel W.; Vaarkamp, Jaap; Cosentino, Francesco (University of Chester, 2018-07-17)
    We have explored applications of Augmented Reality (AR) for external beam radiotherapy to assist with treatment planning, patient education, and treatment delivery. We created an AR development framework for applications in radiotherapy (RADiotherapy Augmented Reality, RAD-AR) for AR ready consumer electronics such as tablet computers and head mounted devices (HMD). We implemented in RAD-AR three tools to assist radiotherapy practitioners with: treatment plans evaluation, patient pre-treatment information/education, and treatment delivery. We estimated accuracy and precision of the patient setup tool and the underlying self-tracking technology, and fidelity of AR content geometric representation, on the Apple iPad tablet computer and the Microsoft HoloLens HMD. Results showed that the technology could already be applied for detection of large treatment setup errors, and could become applicable to other aspects of treatment delivery subject to technological improvements that can be expected in the near future. We performed user feedback studies of the patient education and the plan evaluation tools. Results indicated an overall positive user evaluation of AR technology compared to conventional tools for the radiotherapy elements implemented. We conclude that AR will become a useful tool in radiotherapy bringing real benefits for both clinicians and patients, contributing to successful treatment outcomes.
  • Laser Surface Modification of NiTi for Medical Applications

    Man, Hau-Chung; Lawrence, Jonathan; Avis, Nicholas; Waugh, David G.; Shi, Yu; Ng, Chi-Ho (University of Chester, 2017-11)
    Regarding the higher demand of the total joint replacement (TJR) and revision surgeries in recent years, an implant material should provide much longer lifetime without failure. Nickel titanium (NiTi) is the most popular shape memory alloy in the industry, especially in medical devices due to its unique mechanical properties such as pseudo-elasticity, damping capacity, shape memory and good biocompatibility. However, concerns of nickel ion release of this alloy still exist if it is implanted for a prolonged period of time. Nickel is well known for the possibility of causing allergic response and degeneration of muscle tissue as well as being carcinogenic for the human body beyond a certain threshold. Therefore, drastically improving the surface properties (e.g. wear resistance) of NiTi is a vital step for its adoption as orthopaedic implants. To overcome the above-mentioned risks, different surface treatment techniques have been proposed and investigated, such as Physical Vapour Deposition (PVD), Chemical Vapour Deposition (CVD), ion implantation, plasma spraying, etc. Yet all of these techniques have similar limitations such as high treatment temperature, poor metallurgical bonding between coated film and substrate, and lower flexibility and efficiency. As a result, laser gas nitriding would be an ideal treatment method as it could overcome these drawbacks. Moreover, the shape memory effect and pseudo-elasticity of NiTi from a reversible phase transformation between the martensitic phase and the austenitic phase are very sensitive to heat. Hence, NiTi implant is subjected to the following provisions of the thermo-mechanical treatment process, and this implant provides desired characteristics. It is important to suggest a surface treatment, which would not disturb the original build-in properties. As a result, the low-temperature methods for substrate have to be employed on the surface of NiTi. This present study aims to investigate the feasibility of applying diffusion laser gas nitriding technique to improve the wettability and wear resistance of NiTi as well as establish the optimization technique. The current report summaries the result of laser nitrided NiTi by continuous-wave (CW) fibre laser in nitrogen environment. The microstructure, surface morphology, wettability, wear resistance of the coating layer has been analysed using scanning electron microscopy (SEM), X-ray diffractometry (XRD), sessile drop technique, 3-D profile measurement and reciprocating wear test. The resulting surface layer is free of cracks, and the wetting behaviour is better than the bare NiTi. The wear resistance of the optimised nitride sample with different hatch patterns is also evaluated using reciprocating wear testing against ultra-high-molecular-weight polyethylene (UHMWPE) in Hanks’ solution. The results indicate that the wear rates of the nitride samples and the UHMWPE counter-part were both significantly reduced. It is concluded that the diffusion laser gas nitriding is a potential low-temperature treatment technique to improve the surface properties of NiTi. This technique can be applied to a femoral head or a bone fixation plates with relatively large surface area and movable components.
  • Insights from the parallel implementation of efficient algorithms for the fractional calculus

    Banks, Nicola E. (University of Chester, 2015-07)
    This thesis concerns the development of parallel algorithms to solve fractional differential equations using a numerical approach. The methodology adopted is to adapt existing numerical schemes and to develop prototype parallel programs using the MatLab Parallel Computing Toolbox (MPCT). The approach is to build on existing insights from parallel implementation of ordinary differential equations methods and to test a range of potential candidates for parallel implementation in the fractional case. As a consequence of the work, new insights on the use of MPCT for prototyping are presented, alongside conclusions and algorithms for the effective implementation of parallel methods for the fractional calculus. The principal parallel approaches considered in the work include: - A Runge-Kutta Method for Ordinary Differential Equations including the application of an adapted Richardson Extrapolation Scheme - An implementation of the Diethelm-Chern Algorithm for Fractional Differential Equations - A parallel version of the well-established Fractional Adams Method for Fractional Differential Equations - The adaptation for parallel implementation of Lubich's Fractional Multistep Method for Fractional Differential Equations An important aspect of the work is an improved understanding of the comparative diffi culty of using MPCT for obtaining fair comparisons of parallel implementation. We present details of experimental results which are not satisfactory, and we explain how the problems may be overcome to give meaningful experimental results. Therefore, an important aspect of the conclusions of this work is the advice for other users of MPCT who may be planning to use the package as a prototyping tool for parallel algorithm development: by understanding how implicit multithreading operates, controls can be put in place to allow like-for-like performance comparisons between sequential and parallel programs.
  • Higher Order Numerical Methods for Fractional Order Differential Equations

    Pal, Kamal (University of Chester, 2015-08)
    This thesis explores higher order numerical methods for solving fractional differential equations.
  • Numerical treatment of oscillatory delay and mixed functional differential equations arising in modelling

    Ford, Neville J.; Malique, Md A. (University of Liverpool (University of Chester), 2012-09)
    The pervading theme of this thesis is the development of insights that contribute to the understanding of whether certain classes of functional differential equation have solutions that are all oscillatory. The starting point for the work is the analysis of simple (linear autonomous) ordinary differential equations where existing results allow a full explanation of the phenomena. The Laplace transform features as a key tool in developing a theoretical background. The thesis goes on to explore the corresponding theory for delay equations, advanced equations and functional di erential equations of mixed type. The focus is on understanding the links between the characteristic roots of the underlying equation, and the presence or otherwise of oscillatory solutions. The linear methods are used as a class of numerical schemes which lead to discrete problems analogous to each of the classes of functional differential equation under consideration. The thesis goes on to discuss the insights that can be obtained for discrete problems in their own right, and then considers those new insights that can be obtained about the underlying continuous problem from analysis of the oscillatory behaviour of the analogous discrete problem. The main conclusions of the work are some semi-automated computational approaches (based upon the Principle of the Argument) which allow the prediction of oscillatory solutions to be made. Examples of the effectiveness of the approach are provided, and there is some discussion of its theoretical basis. The thesis concludes with some observations about further work and some of the limitations of existing analytical insights which restrict the reliability with which the approach developed can be applied to wider classes of problem.
  • Computational and mathematical modelling of plant species interactions in a harsh climate

    Lumb, Patricia M.; Potter, Jacqueline; Ford, Neville J.; Ekaka-A, Enu-Obari N. (University of Liverpool (University of Chester), 2009-07)
    This thesis will consider the following assumptions which are based on a few insights about the artic climate: (1)the artic climate can be characterised by a growing season called summer and a dormat season called winter (2)in the summer season growing conditions are reasonably favourable and species are more likely to compete for plentiful resources (3)in the winter season there would be no further growth and the plant populations would instead by subjected to fierce weather events such as storms which is more likely to lead to the destruction of some or all of the biomass. Under these assumptions, is it possible to find those change in the environment that might cause mutualism (see section 1.9.2) from competition (see section 1.9.1) to change? The primary aim of this thesis to to provide a prototype simulation of growth of two plant species in the artic that: (1)take account of different models for summer and winter seasons (2)permits the effects of changing climate to be seen on each type of plant species interaction.
  • The numerical solution of fractional and distributed order differential equations

    Ford, Neville J.; Edwards, John T.; Connolly, Joseph A. (University of Liverpool (University College Chester), 2004-12)
    Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods. The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs. We then present: 1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and give recommendations for which method is best for any given FDE. 2. a new method for the solution of a non-linear Multi-term Fractional Dif¬ferential Equation. 3. a sequence of methods for the numerical solution of a Distributed Order Differential Equation. 4. a discussion of the problems associated with producing a computer program for obtaining the optimum numerical method for any given FDE.
  • Noise induced changes to dynamic behaviour of stochastic delay differential equations

    Ford, Neville J.; Norton, Stewart J. (University of Liverpool (University of Chester)University of Chester, 2008-02)
    This thesis is concerned with changes in the behaviour of solutions to parameter-dependent stochastic delay differential equations.
  • Numerical analysis of some integral equations with singularities

    Ford, Neville J.; Thomas, Sophy M. (University of Liverpool (Chester College of Higher Education), 2006-04)
    In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.
  • Delay differential equations: Detection of small solutions

    Ford, Neville J.; Lumb, Patricia M. (University of Liverpool (Chester College of Higher Education)University College Chester, 2004-04)
    This thesis concerns the development of a method for the detection of small solutions to delay differential equations. The detection of small solutions is important because their presence has significant influence on the analytical prop¬erties of an equation. However, to date, analytical methods are of only limited practical use. Therefore this thesis focuses on the development of a reliable new method, based on finite order approximations of the underlying infinite dimen¬sional problem, which can detect small solutions. Decisions (concerning the existence, or otherwise, of small solutions) based on our visualisation technique require an understanding of the underlying methodol¬ogy behind our approach. Removing this need would be attractive. The method we have developed can be automated, and at the end of the thesis we present a prototype Matlab code for the automatic detection of small solutions to delay differential equations.
  • A critical evaluation of students' attitudes to electronic learning at the University of Chester

    Shaylor, Jan P.; Wheeler, Timothy J.; Rayner, Linda A. (University of Liverpool (Chester College of Higher Education)University of Chester, 2007-01)
    The research described in this thesis reports the results of a study into the adoption of e-learning strategies based on the use of the World Wide Web (WWW) and Internet. Through an extensive and critical literature review, it exemplifies how higher education uses intranets to deliver learning and support services to their student population. The overall aim of this research was to investigate how e-learning at the University of Chester might more effectively support students' learning needs, thereby improving their experience of e-learning. Students were given a mode of study, either face-to-face (64 subjects) or experimental using online intranet delivery (66 subjects). The course used for this study was a 13 week, Level Two undergraduate computer course taken by non-computing students. Quantitative and qualitative data were collected and analysed. The results reveal significant differences between the performance of the e-learning and face-to-face groups with e-learning students performing poorly when compared to their face-to-face peers. A lack of responsiveness in tutor support and student motivation were established as being major contributing factors as well as differences in the students' individual learning profiles. The research concludes that e-learning, although promoted as being anytime and anywhere is limited in its flexibility and responsiveness in the context in which it was assessed. Most e-learning activities at the University of Chester can be described as 'one size fits all'. They require students to read printed text, carry out further work, research or exercises, and post written comments to a discussion board. There is little evidence that individual student needs and preferences are being considered or supported. With the move towards blended learning in educational institutions, e-learning strategies are being used as a regular part of the curriculum to enhance the student experience. This research provides alternatives for the development and delivery of more individually tailored e-learning courses and provides strategies for supporting students in virtual environments more effectively. The thesis concludes by proposing a new model for e-learning based on these results coupled with a self-critical review and proposals for further research.