• Concerning periodic solutions to non-linear discrete Volterra equations with finite memory

      Baker, Christopher T. H.; Song, Yihong; University of Chester (University of Chester, 2007)
      In this paper we discuss the existence of periodic solutions of discrete (and discretized) non-linear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The “summation” equations studied here can arise as discrete models in their own right but are (as we demonstrate) of a type that arise from the discretization of such integral equations. Our main results are in two parts: (i) results for discrete equations and (ii) consequences for quadrature methods applied to integral equations. The first set of results are obtained using a variety of fixed point theorems. The second set of results address the preservation of properties of integral equations on discretizing them. An expository style is adopted and examples are given to illustrate the discussion.
    • Controller Design Methodology for Sustainable Local Energy Systems

      Counsell, John M.; Al-Khaykan, A. (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).
    • 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.
    • Efficient Surrogate Model-Assisted Evolutionary Algorithm for Electromagnetic Design Automation with Applications

      Akinsolu, Mobayode, O. (University of ChesterWrexham Glyndŵr UniversityWrexham Glyndwr University, 2019-10)
      In this thesis, the surrogate model-aware evolutionary search (SMAS) framework is extended for efficient interactive optimisation of multiple criteria electromagnetic (EM) designs and/or devices through a novel method called two-stage interactive efficient EM micro-actuator design optimisation (TIEMO). The first robust analytical and behavioural study of the SMAS framework is also carried out in this thesis to serve as a guide for the meticulous selection of multiple differential evolution (DE) mutation strategies to make SMAS fit for use in parallel computing environments. Based on the study of SMAS and the self-adaptive use of the selected multiple DE mutation strategies and reinforcement learning techniques, a novel method, parallel surrogate model-assisted evolutionary algorithm for EM design (PSAED) is proposed. PSAED is tested extensively using mathematical benchmark problems and numerical EM design problems. For all cases, the efficiency improvement of PSAED compared to state-of-the-art evolutionary algorithms (EAs) is demonstrated by the several times up to about 20 times speed improvement observed and the high quality of design solutions. PSAED is then applied to real-world EM design problems as two purposebuilt methods for antenna design and optimisation and high-performance microelectro-mechanical systems (MEMS) design and optimisation in parallel computing environments, parallel surrogate model-assisted hybrid DE for antenna optimisation (PSADEA) and adaptive surrogate model-assisted differential evolution for MEMS optimisation (ASDEMO), respectively. For all the real-world antenna and MEMS design cases, PSAED methods obtain very satisfactory design solutions using an affordable optimisation time and comparisons are made with available alternative methods. Results from the comparisons show that PSAED methods obtain very satisfactory design solutions in all runs using an affordable optimisation time in each, whereas the alternative methods fail and/or seldom succeed to obtain feasible or satisfactory design solutions. PSAED methods also show better robustness and stability. In the future, PSAED methods will be embedded into commercial CAD/CEM tools and will be further extended for use in higher-order parallel clusters.
    • Existence theory for a class of evolutionary equations with time-lag, studied via integral equation formulations

      Baker, Christopher T. H.; Lumb, Patricia M.; University of Chester (University of Chester, 2006)
      In discussions of certain neutral delay differential equations in Hale’s form, the relationship of the original problem with an integrated form (an integral equation) proves to be helpful in considering existence and uniqueness of a solution and sensitivity to initial data. Although the theory is generally based on the assumption that a solution is continuous, natural solutions of neutral delay differential equations of the type considered may be discontinuous. This difficulty is resolved by relating the discontinuous solution to its restrictions on appropriate (half-open) subintervals where they are continuous and can be regarded as solutions of related integral equations. Existence and unicity theories then follow. Furthermore, it is seen that the discontinuous solutions can be regarded as solutions in the sense of Caratheodory (where this concept is adapted from the theory of ordinary differential equations, recast as integral equations).
    • An experimental and computational investigation of pressurised anaerobic digestion

      Wilkinson, Steve; Liang, Zhixuan (University of Chester, 2021-01)
      The aim of this work is to gain a greater understanding of the effect of headspace pressure on biogas production from anaerobic digestion. This is important to improve the energy content of the biogas i.e., increase the methane content and therefore reduce the need for upgrading to scrub out carbon dioxide. In addition, headspace pressure can potentially be used to provide energy for mixing and gas sparging, thereby removing the need for mechanical agitation. In this work, an existing computational model was adapted to investigate its prediction of the variation of biogas production as headspace pressure is increased above atmospheric. The simulation results were accompanied with experimental work using periodic venting of sealed laboratory bottles. The headspace pressure was inferred from the weight loss during venting to atmosphere. In addition, a fully instrumented, pressurised digestor system was designed and constructed in which headspace pressure could be measured directly. Experiments were conducted with headspace pressures of up to 3.4 barg. The biogas that accumulated in the headspace during the digestion process was sampled periodically to determine its composition. The results showed that biogas produced at higher pressures has a higher methane content. A mass balance for the headspace sampling process, which assumed no gas was released from the liquid during sampling, was compared to experimental measurements. This led to the discovery that the effective Henry’s constant for the solubility of carbon dioxide could be an order of magnitude lower in digestate than the known value for pure water. Both the adapted model and the laboratory-scale experiments showed that as the headspace pressure increases, the production rate of biogas decreases. The adapted model also gives slightly higher methane content for higher pressure. The model was then used to estimate the specific growth rates of bacteria used in the laboratory-scale experiments and the agreement was not good, which indicates further changes to the model are needed. The results show that the rate of biogas production reduces as the headspace pressure increases but the rate of decrease is not very steep. This same trend was also displayed for yeast fermentation, which was also studied as another model process for pressurised biological gas production. The variation of the rate of 𝐶𝑂2 evolution with pressure was also used to infer the concentration of dissolved 𝐶𝑂2 within the fermenting yeast cells. Finally, turning attention back to anaerobic digestion processes for energy, it is encouraging that at the relatively modest elevation of pressure required for sparging to give mixing (less than 0.5 barg), the reduction in biogas evolution is small. This small penalty might therefore be offset in a production scale system by the reduced costs of mixing and increased methane content of the biogas.
    • 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.
    • 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.
    • Fixed point theroms and their application - discrete Volterra applications

      Baker, Christopher T. H.; Song, Yihong; University of Chester (University of Chester, 2006)
      The existence of solutions of nonlinear discrete Volterra equations is established. We define discrete Volterra operators on normed spaces of infinite sequences of finite-dimensional vectors, and present some of their basic properties (continuity, boundedness, and representation). The treatment relies upon the use of coordinate functions, and the existence results are obtained using fixed point theorems for discrete Volterra operators on infinite-dimensional spaces based on fixed point theorems of Schauder, Rothe, and Altman, and Banach’s contraction mapping theorem, for finite-dimensional spaces.
    • A Framework for Web-Based Immersive Analytics

      John, Nigel; Ritsos, Panagiotis; Butcher, Peter W. S. (University of Chester, 2020-08-17)
      The emergence of affordable Virtual Reality (VR) interfaces has reignited the interest of researchers and developers in exploring new, immersive ways to visualise data. In particular, the use of open-standards Web-based technologies for implementing VR experiences in a browser aims to enable their ubiquitous and platform-independent adoption. In addition, such technologies work in synergy with established visualization libraries, through the HTML Document Object Model (DOM). However, creating Immersive Analytics (IA) experiences remains a challenging process, as the systems that are currently available require knowledge of game engines, such as Unity, and are often intrinsically restricted by their development ecosystem. This thesis presents a novel approach to the design, creation and deployment of Immersive Analytics experiences through the use of open-standards Web technologies. It presents <VRIA>, a Web-based framework for creating Immersive Analytics experiences in VR that was developed during this PhD project. <VRIA> is built upon WebXR, A-Frame, React and D3.js, and offers a visualization creation workflow which enables users of different levels of expertise to rapidly develop Immersive Analytics experiences for the Web. The aforementioned reliance on open standards and the synergies with popular visualization libraries make <VRIA> ubiquitous and platform-independent in nature. Moreover, by using WebXR’s progressive enhancement, the experiences <VRIA> is able to create are accessible on a plethora of devices. This thesis presents an elaboration on the motivation for focusing on open-standards Web technologies, presents the <VRIA> visualization creation workflow and details the underlying mechanics of our framework. It reports on optimisation techniques, integrated into <VRIA>, that are necessary for implementing Immersive Analytics experiences with the necessary performance profile on the Web. It discusses scalability implications of the framework and presents a series of use case applications that demonstrate the various features of <VRIA>. Finally, it describes the lessons learned from the development of the framework, discusses current limitations, and outlines further extensions.
    • Group rings: Units and their applications in self-dual codes

      Gildea, Joe; Taylor, Rhian (University of Chester, 2021-03)
      The initial research presented in this thesis is the structure of the unit group of the group ring Cn x D6 over a field of characteristic 3 in terms of cyclic groups, specifically U(F3t(Cn x D6)). There are numerous applications of group rings, such as topology, geometry and algebraic K-theory, but more recently in coding theory. Following the initial work on establishing the unit group of a group ring, we take a closer look at the use of group rings in algebraic coding theory in order to construct self-dual and extremal self-dual codes. Using a well established isomorphism between a group ring and a ring of matrices, we construct certain self-dual and formally self-dual codes over a finite commutative Frobenius ring. There is an interesting relationships between the Automorphism group of the code produced and the underlying group in the group ring. Building on the theory, we describe all possible group algebras that can be used to construct the well-known binary extended Golay code. The double circulant construction is a well-known technique for constructing self-dual codes; combining this with the established isomorphism previously mentioned, we demonstrate a new technique for constructing self-dual codes. New theory states that under certain conditions, these self-dual codes correspond to unitary units in group rings. Currently, using methods discussed, we construct 10 new extremal self-dual codes of length 68. In the search for new extremal self-dual codes, we establish a new technique which considers a double bordered construction. There are certain conditions where this new technique will produce self-dual codes, which are given in the theoretical results. Applying this new construction, we construct numerous new codes to verify the theoretical results; 1 new extremal self-dual code of length 64, 18 new codes of length 68 and 12 new extremal self-dual codes of length 80. Using the well established isomorphism and the common four block construction, we consider a new technique in order to construct self-dual codes of length 68. There are certain conditions, stated in the theoretical results, which allow this construction to yield self-dual codes, and some interesting links between the group ring elements and the construction. From this technique, we construct 32 new extremal self-dual codes of length 68. Lastly, we consider a unique construction as a combination of block circulant matrices and quadratic circulant matrices. Here, we provide theory surrounding this construction and conditions for full effectiveness of the method. Finally, we present the 52 new self-dual codes that result from this method; 1 new self-dual code of length 66 and 51 new self-dual codes of length 68. Note that different weight enumerators are dependant on different values of β. In addition, for codes of length 68, the weight enumerator is also defined in terms of γ, and for codes of length 80, the weight enumerator is also de ned in terms of α.
    • Halanay-type theory in the context of evolutionary equations with time-lag

      Baker, Christopher T. H.; University of Chester (University of Chester, 2009)
      We consider extensions and modifications of a theory due to Halanay, and the context in which such results may be applied. Our emphasis is on a mathematical framework for Halanay-type analysis of problems with time lag and simulations using discrete versions or numerical formulae. We present selected (linear and nonlinear, discrete and continuous) results of Halanay type that can be used in the study of systems of evolutionary equations with various types of delayed argument, and the relevance and application of our results is illustrated, by reference to delay-differential equations, difference equations, and methods.
    • 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.
    • 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.
    • Interactive Three-Dimensional Simulation and Visualisation of Real Time Blood Flow in Vascular Networks

      John, Nigel; Pop, Serban; Holland, Mark, I (University of ChesterUnviersity of Chester, 2020-05)
      One of the challenges in cardiovascular disease management is the clinical decision-making process. When a clinician is dealing with complex and uncertain situations, the decision on whether or how to intervene is made based upon distinct information from diverse sources. There are several variables that can affect how the vascular system responds to treatment. These include: the extent of the damage and scarring, the efficiency of blood flow remodelling, and any associated pathology. Moreover, the effect of an intervention may lead to further unforeseen complications (e.g. another stenosis may be “hidden” further along the vessel). Currently, there is no tool for predicting or exploring such scenarios. This thesis explores the development of a highly adaptive real-time simulation of blood flow that considers patient specific data and clinician interaction. The simulation should model blood realistically, accurately, and through complex vascular networks in real-time. Developing robust flow scenarios that can be incorporated into the decision and planning medical tool set. The focus will be on specific regions of the anatomy, where accuracy is of the utmost importance and the flow can develop into specific patterns, with the aim of better understanding their condition and predicting factors of their future evolution. Results from the validation of the simulation showed promising comparisons with the literature and demonstrated a viability for clinical use.
    • An inverse problem for delay differential equations - analysis via integral equations

      Baker, Christopher T. H.; Parmuzin, Evgeny I.; University of Chester (University of Chester, 2006)
    • 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.
    • 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.
    • Mathematical Modelling of DNA Methylation

      Roberts, Jason; Zagkos, Loukas (University of Chester, 2020-03-09)
      DNA methylation is a key epigenetic process which has been intimately associated with gene regulation. In recent years growing evidence has associated DNA methylation status with a variety of diseases including cancer, Alzheimer’s disease and cardiovascular disease. Moreover, changes to DNA methylation have also recently been implicated in the ageing process. The factors which underpin DNA methylation are complex, and remain to be fully elucidated. Over the years mathematical modelling has helped to shed light on the dynamics of this important molecular system. Although the existing models have contributed significantly to our overall understanding of DNA methylation, they fall short of fully capturing the dynamics of this process. In this work DNA methylation models are developed and improved and their suitability is demonstrated through mathematical analysis and computational simulation. In particular, a linear and nonlinear deterministic model are developed which capture more fully the dynamics of the key intracellular events which characterise DNA methylation. Furthermore, uncertainty is introduced into the model to describe the presence of intrinsic and extrinsic cell noise. This way a stochastic model is constructed and presented which accounts for the stochastic nature in cell dynamics. One of the key predictions of the model is that DNA methylation dynamics do not alter when the quantity of DNA methylation enzymes change. In addition, the nonlinear model predicts DNA methylation promoter bistability, which is commonly observed experimentally. Moreover, a new way of modelling DNA methylation uncertainty is introduced.
    • Mixed-type functional differential equations: A numerical approach (extended version)

      Ford, Neville J.; Lumb, Patricia M.; University of Chester (University of Chester, 2007)