• Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

      Baker, Christopher T. H.; Buckwar, Evelyn; Univesity College Chester ; Humboldt-Universität zu Berlin (Elsevier, 2005-12-15)
      This article carries out an analysis which proceeds as follows: showing that an inequality of Halanay type (derivable via comparison theory) can be employed to derive conditions for p-th mean stability of a solution; producing a discrete analogue of the Halanay-type theory, that permits the development of a p-th mean stability analysis of analogous stochastic difference equations. The application of the theoretical results is illustrated by deriving mean-square stability conditions for solutions and numerical solutions of a constant-coefficient linear test equation.
    • Extending an Established Isomorphism between Group Rings and a Subring of the n × n Matrices

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; University of Scranton; University of Chester
      In this work, we extend an established isomorphism between group rings and a subring of the n × n matrices. This extension allows us to construct more complex matrices over the ring R. We present many interesting examples of complex matrices constructed directly from our extension. We also show that some of the matrices used in the literature before can be obtained by a direct application of our extended isomorphism.
    • Fabrication of Graphene Oxide Supercapacitor Devices

      Down, Michael P.; Rowley-Neale, Samuel J.; Smith, Graham C.; Banks, Craig E. (American Chemical Society (ACS), 2018-02-14)
    • 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.
    • Fibre laser joining of dissimilar materials: Commercially pure Ti and PET hybrid joint for medical device applications

      Chan, Chi-Wai; Smith, Graham C.; Queen's University Belfast; University of Chester (Elsevier, 2016-04-29)
      Laser transmission joining (LTJ) is growing in importance, and has the potential to become a niche technique for the fabrication of hybrid plastic-metal joints for medical device applications. The possibility of directly joining plastics to metals by LTJ has been demonstrated by a number of recent studies. However, a reliable and quantitative method for defining the contact area between the plastic and metal, facilitating calculation of the mechanical shear stress of the hybrid joints, is still lacking. A new method, based on image analysis using ImageJ, is proposed here to quantify the contact area at the joint interface. The effect of discolouration on the mechanical performance of the hybrid joints is also reported for the first time. Biocompatible polyethylene terephthalate (PET) and commercially pure titanium (Ti) were selected as materials for laser joining using a 200 W CW fibre laser system. The effect of laser power, scanning speed and stand-off distance between the nozzle tip and top surface of the plastic were studied and analysed by Taguchi L9 orthogonal array and ANOVA respectively. The surface morphology, structure and elemental composition on the PET and Ti surfaces after shearing/peeling apart were characterized by SEM, EDX, XRD and XPS.
    • Fibre Laser Nitriding of Titanium and its Alloy in Open Atmosphere for Orthopaedic Implant Applications: Investigations on Surface Quality, Microstructure and Tribological Properties

      Chan, Chi-Wai; Lee, Seunghwan; Smith, Graham C.; Donaghy, Clare L.; Queens University Belfast (Chan, Donaghy), Technical University Denmark (Lee), University of Chester (Smith) (Elsevier, 2016-12-20)
      Laser nitriding is known to be an effective method to improve the surface hardness and wear resistance of titanium and its alloys. However, the process requires a gas chamber and this greatly limits the practicability for treating orthopaedic implants which involve complex-shaped parts or curved surfaces, such as the tapered surface in a femoral stemor the ball-shaped surface in a femoral head. To tackle this problem, a direct laser nitriding process in open atmosphere was performed on commercially pure titanium (grade 2, TiG2) and Ti6Al4V alloy (grade 5, TiG5) using a continuous-wave (CW) fibre laser. The effects of varying process parameters, for instance laser power and nitrogen pressure on the surface quality, namely discolouration were quantified using ImageJ analysis. The optimised process parameters to produce the gold-coloured nitride surfaces were also identified: 40W(laser power), 25mm/s (scanning speed), 1.5mm(standoff distance) and 5 bar (N2 pressure). Particularly, N2 pressure at 5 barwas found to be the threshold above which significant discolouration will occur. The surface morphology, composition, microstructure, micro-hardness, and tribological properties, particularly hydrodynamic size distribution of wear debris, were carefully characterized and compared. The experimental results showed that TiG2 and TiG5 reacted differently with the laser radiation at 1.06 μm wavelength in laser nitriding as evidenced by substantial differences in the microstructure, and surface colour and morphology. Furthermore, both friction andwear properties were strongly affected by the hardness and microstructure of titaniumsamples and direct laser nitriding led to substantial improvements in their wear resistant properties. Between the two types of titanium samples, bare TiG2 showed higher friction forces and wear rates, but this trend was reversed after laser nitriding treatments.
    • Fibre laser treatment of beta TNZT titanium alloys for load-bearing implant applications: Effects of surface physical and chemical features on mesenchymal stem cell response and Staphylococcus aureus bacterial attachment

      Donaghy, Clare L.; McFadden, Ryan; Smith, Graham C.; Kelaini, Sophia; Carson, Louise; Malinov, Savko; Margariti, Andriana; Chan, Chi-Wai; Queens University Belfast; University of Chester (MDPI, 2019-03-12)
      A mismatch in bone and implant elastic modulus can lead to aseptic loosening and ultimately implant failure. Selective elemental composition of titanium (Ti) alloys coupled with surface treatment can be used to improve osseointegration and reduce bacterial adhesion. The biocompatibility and antibacterial properties of Ti-35Nb-7Zr-6Ta (TNZT) using fibre laser surface treatment were assessed in this work, due to its excellent material properties (low Young’s modulus and non-toxicity) and the promising attributes of fibre laser treatment (very fast, non-contact, clean and only causes changes in surface without altering the bulk composition/microstructure). The TNZT surfaces in this study were treated in a high speed regime, specifically 100 and 200 mm/s, (or 6 and 12 m/min). Surface roughness and topography (WLI and SEM), chemical composition (SEM-EDX), microstructure (XRD) and chemistry (XPS) were investigated. The biocompatibility of the laser treated surfaces was evaluated using mesenchymal stem cells (MSCs) cultured in vitro at various time points to assess cell attachment (6, 24 and 48 h), proliferation (3, 7 and 14 days) and differentiation (7, 14 and 21 days). Antibacterial performance was also evaluated using Staphylococcus aureus (S. aureus) and Live/Dead staining. Sample groups included untreated base metal (BM), laser treated at 100 mm/s (LT100) and 200 mm/s (LT200). The results demonstrated that laser surface treatment creates a rougher (Ra value of BM is 199 nm, LT100 is 256 nm and LT200 is 232 nm), spiky surface (Rsk > 0 and Rku > 3) with homogenous elemental distribution and decreasing peak-to-peak distance between ripples (0.63 to 0.315 m) as the scanning speed increases (p < 0.05), generating a surface with distinct micron and nano scale features. The improvement in cell spreading, formation of bone-like nodules (only seen on the laser treated samples) and subsequent four-fold reduction in bacterial attachment (p < 0.001) can be attributed to the features created through fibre laser treatment, making it an excellent choice for load bearing implant applications. Last but not least, the presence of TiN in the outermost surface oxide might also account for the improved biocompatibility and antibacterial performances of TNZT.
    • Fibre laser treatment of martensitic NiTi alloys for load-bearing implant applications: Effects of surface chemistry on inhibiting Staphylococcus aureus biofilm formation

      Smith, Graham C.; Chan, Chi-Wai; Carson, Louise; Queens University Belfast; University of Chester (Elsevier, 2018-06-15)
      Biofilm infection is one of the main reasons for implant failure. It is extremely difficult to cure due to its high resistance to antibiotic treatments, and can result in substantial healthcare costs. In this study, the important shape memory NiTi alloy, in its martensitic state, was laser-treated using our newly-developed surface modification technique, aiming to tackle the biofilm infection problem. Martensitic NiTi was chosen for investigation because of its potential advantages in terms of (i) lower elastic modulus and (ii) higher damping capacity over its austenitic counterpart, giving rise to a lower risk of stress shielding and maximum stress between bones and load-bearing implants. The surfaces after laser treatment were systemically analysed using a series of surface measurement (i.e. surface roughness and water contact angle) and material characterisation (i.e. SEM-EDX, XRD and XPS) techniques. The antibacterial performance of the laser-treated surfaces was evaluated using the Staphylococcus aureus (or S. aureus) cells in-vitro cultured at 37 oC for 24h. Fluorescence microscopy accompanied by Live/Dead staining was employed to analyse the cell culture results. The surfaces in their as-received states and after polishing were also tested and compared with the laser-treated surfaces in order to gain a deeper insight in how different surface conditions would influence biofilm formation. Our results indicate that the surfaces after laser treatment can mitigate bacterial attachment and biofilm formation effectively. The antibacterial performance was mainly attributable to the laser-formed oxides which brought desirable changes to the surface chemistry of NiTi. The laser-induced changes in surface roughness and topography, on a micrometre scale, only played a minor role in influencing bacterial attachment. The findings of this study demonstrated for the first time that martensitic NiTi with laser treatment could be a promising choice for the next-generation implants given its superior antimicrobial resistance and favourable mechanical properties for loading bearing applications.
    • Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations

      Pal, Kamal; Liu, Fang; Yan, Yubin; Roberts, Graham; University of Chester (Springer International Publishing, 2015-06-17)
      Finite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),10 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence.
    • A finite element analysis of impact damage in composite laminates

      Shi, Yu; Soutis, Constantinos; University of Chester; University of Manchester (Cambridge University Press, 2012-12-01)
      In this work, stress-based and fracture mechanics criteria were developed to predict initiation and evolution, respectively, of intra- and inter-laminar cracking developed in composite laminates subjected to low velocity impact. The Soutis shear stress-strain semi-empirical model was used to describe the nonlinear shear behaviour of the composite. The damage model was implemented in the finite element (FE) code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Delamination (or inter-laminar cracking) was modelled using interface cohesive elements and the splitting and transverse matrix cracks that appeared within individual plies were also simulated by inserting cohesive elements between neighbouring elements parallel to the fibre direction in each single layer. A good agreement was obtained when compared the numerically predicted results to experimentally obtained curves of impact force and absorbed energy versus time. A non-destructive technique (NDT), penetrant enhanced X-ray radiography, was used to observe the various damage mechanisms induced by impact. It has been shown that the proposed damage model can successfully capture the internal damage pattern and the extent to which it was developed in these carbon fibre/epoxy composite laminates.
    • A finite element method for time fractional partial differential equations

      Ford, Neville J.; Xiao, Jingyu; Yan, Yubin; University of Chester ; Harbin Institute of Technology ; University of Chester (2011-09-01)
      This article considers the finite element method for time fractional differential equations.
    • Finite-time blow-up of a non-local stochastic parabolic problem

      Kavallaris, Nikos I.; Yan, Yubin; University of Chester (Elsevier, 2020-04-13)
      The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for such problem. The first part of the manuscript deals with the investigation of the conditions which guarantee the occurrence of noise-induced blow-up. In the second part we first prove the $C^{1}$-spatial regularity of the solution. Then, based on this regularity result, and using a strong positivity result we derive, for first in the literature of SPDEs, a Hopf's type boundary value point lemma. The preceding results together with Kaplan's eigenfunction method are then employed to provide a (non-local) drift term induced blow-up result. In the last part of the paper, we present a method which provides an upper bound of the probability of (non-local) drift term induced blow-up.
    • 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.
    • Flicker mitigation strategy for a doubly fed induction generator by torque control

      Zhang, Yunqian Q.; Hu, Weihao; Chen, Zhe; Cheng, Ming; Hu, Yanting (IET, 2014-03)
      Owing to the rotational sampling of turbulence, wind shear and tower shadow effects grid connected variable speed wind turbines could lead to the power fluctuations which may produce flicker during continuous operation. A model of an megawatt (MW)-level variable speed wind turbine with a doubly fed induction generator is presented to investigate the flicker mitigation. Taking advantage of the large inertia of the wind turbine rotor, a generator torque control (GTC) strategy is proposed, so that the power oscillation is stored as the kinetic energy of the wind turbine rotor, thus the flicker emission could be reduced. The GTC scheme is proposed and designed according to the generator rotational speed. The simulations are performed on the national renewable energy laboratory 1.5 MW upwind reference wind turbine model. Simulation results show that damping the generator active power by GTC is an effective means for flicker mitigation of variable speed wind turbines during continuous operation. keywords: {asynchronous generators;oscillations;power generation control;torque control;wind power plants;wind turbines;GTC strategy;continuous operation;doubly fed induction generator;flicker emission;flicker mitigation strategy;generator active power;generator torque control;kinetic energy;megawatt-level variable speed wind turbine;power oscillation;tower shadow effects grid connected variable speed wind turbines;turbulence;upwind reference wind turbine model;variable speed wind turbines;wind shear;wind turbine rotor
    • Formal Verification of Astronaut-Rover Teams for Planetary Surface Operations

      Webster, Matt; Dennis, Louise A; Dixon, Clare; Fisher, Michael; Stocker, Richard; Sierhuis, Maarten; University of Liverpool; University of Chester; Ejenta, inc.
      This paper describes an approach to assuring the reliability of autonomous systems for Astronaut-Rover (ASRO) teams using the formal verification of models in the Brahms multi-agent modelling language. Planetary surface rovers have proven essential to several manned and unmanned missions to the moon and Mars. The first rovers were tele- or manuallyoperated, but autonomous systems are increasingly being used to increase the effectiveness and range of rover operations on missions such as the NASA Mars Science Laboratory. It is anticipated that future manned missions to the moon and Mars will use autonomous rovers to assist astronauts during extravehicular activity (EVA), including science, technical and construction operations. These ASRO teams have the potential to significantly increase the safety and efficiency of surface operations. We describe a new Brahms model in which an autonomous rover may perform several different activities including assisting an astronaut during EVA. These activities compete for the autonomous rovers “attention’ and therefore the rover must decide which activity is currently the most important and engage in that activity. The Brahms model also includes an astronaut agent, which models an astronauts predicted behaviour during an EVA. The rover must also respond to the astronauts activities. We show how this Brahms model can be simulated using the Brahms integrated development environment. The model can then also be formally verified with respect to system requirements using the SPIN model checker, through automatic translation from Brahms to PROMELA (the input language for SPIN). We show that such formal verification can be used to determine that mission- and safety critical operations are conducted correctly, and therefore increase the reliability of autonomous systems for planetary rovers in ASRO teams.
    • Fourier spectral methods for some linear stochastic space-fractional partial differential equations

      Liu, Yanmei; Khan, Monzorul; Yan, Yubin; LuLiang University; University of Chester (MDPI, 2016-07-01)
      Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in one-dimensional case are introduced and analyzed. The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject to some boundary conditions. We approximate the space-time white noise by using piecewise constant functions and obtain the approximated stochastic space-fractional partial differential equations. The approximated stochastic space-fractional partial differential equations are then solved by using Fourier spectral methods. Error estimates in $L^{2}$- norm are obtained. Numerical examples are given.
    • Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises

      Liu, Fang; Yan, Yubin; Khan, Monzorul; Lvliang University, University of Chester (EudoxusPress, 2018-02-28)
      Fourier spectral methods for solving stochastic space fractional partial differential equations driven by special additive noises in one-dimensional case are introduced and analyzed. The space fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject to some boundary conditions. The space-time noise is approximated by the piecewise constant functions in the time direction and by some appropriate approximations in the space direction. The approximated stochastic space fractional partial differential equations are then solved by using Fourier spectral methods. For the linear problem, we obtain the precise error estimates in the $L_{2}$ norm and find the relations between the error bounds and the fractional powers. For the nonlinear problem, we introduce the numerical algorithms and MATLAB codes based on the FFT transforms. Our numerical algorithms can be adapted easily to solve other stochastic space fractional partial differential equations with multiplicative noises. Numerical examples for the semilinear stochastic space fractional partial differential equations are given.
    • Fractional boundary value problems: Analysis and numerical methods

      Ford, Neville J.; Morgado, Maria L.; University of Chester ; University of Tras-os-Montes e Alto Douro (Springer, 2011-07-28)
      This journal article discusses nonlinear boundary value problems.
    • Fractional pennes' bioheat equation: Theoretical and numerical studies

      Ferras, Luis L.; Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S.; Nobrega, Joao M.; University of Minho & University of Chester, University of Chester, UTAD, UNL Lisboa, University of Minho (de Gruyter, 2015-08-04)
      In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bio heat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.
    • 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.