• Panel adjustment and error analysis for a large active main reflector antenna by using the panel adjustment matrix

      Lian, Peiyuan; Wang, Congsi; Xue, Song; Xu, Qian; Wang, Na; xiang, Binbin; Shi, Yu; Jia, Yu; Xidian University; University of Chester; Aston University; Chinese Academy of Sciences
      Active panels are generally applied in large aperture and high frequency reflector antennas, and the precise calculation of the actuator adjustment value is of great importance. First, the approximation relationship between the adjustment value and panel elastic deformation is established. Subsequently, a panel adjustment matrix for the whole reflector is derived to calculate the reflector deformation caused by the actuator adjustment. Next, the root mean square (rms) error of the deformed reflector is expressed as a quadratic form in the matrix form, and the adjustment value can be derived easily and promptly from the corresponding extreme value. The solution is expected to be unique and optimal since the aforementioned quadratic form is a convex function. Finally, a 35 m reflector antenna is adopted to perform the panel adjustments, and the effect of the adjustment errors is discussed. The results show that compared to the traditional model, where the panel elastic deformation is not considered, the proposed method exhibits a higher accuracy and is more suitable for use in large reflectors with a high operation frequency. The adjustment errors in different rings exert different influences on the gain and sidelobe level, which can help determine the actuator distribution with different precisions.
    • Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; Kaya, Abidin; University of Scranton; University of Chester; Harmony School of Technology (Springer, 2021-05-19)
      In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a composite G-code is also a composite G-code. We also define quasi-composite G-codes. Additionally, we study generator matrices, which consist of the identity matrices and the composite matrices. Together with the generator matrices, the well known extension method, the neighbour method and its generalization, we find extremal binary self-dual codes of length 68 with new weight enumerators for the rare parameters $\gamma$ = 7; 8 and 9: In particular, we find 49 new such codes. Moreover, we show that the codes we find are inaccessible from other constructions.
    • High order algorithms for numerical solution of fractional differential equations

      Asl, Mohammad Shahbazi; Javidi, Mohammad; Yan, Yubin; University of Chester; University of Tabriz
      In this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.
    • Terahertz reading of ferroelectric domain wall dielectric switching

      Zhang, Man; Chen, Zhe; Yue, Yajun; Chen, Tao; Yan, Zhongna; Jiang, Qinghui; Yang, Bin; Eriksson, Mirva; Tang, Jianhua; Zhang, Dou; et al.
      Ferroelectric domain walls (DWs) are important nano scale interfaces between two domains. It is widely accepted that ferroelectric domain walls work idly at terahertz (THz) frequencies, consequently discouraging efforts to engineer the domain walls to create new applications that utilise THz radiation. However, the present work clearly demonstrates the activity of domain walls at THz frequencies in a lead free Aurivillius phase ferroelectric ceramic, Ca0.99Rb0.005Ce0.005Bi2Nb2O9, examined using THz time domain spectroscopy (THz-TDS). The dynamics of domain walls are different at kHz and THz frequencies. At low frequencies, domain walls work as a group to increase dielectric permittivity. At THz frequencies, the defective nature of domain walls serves to lower the overall dielectric permittivity. This is evidenced by higher dielectric permittivity in the THz band after poling, reflecting decreased domain wall density. An elastic vibrational model has also been used to verify that a single frustrated dipole in a domain wall represents a weaker contribution to the permittivity than its counterpart within a domain. The work represents a fundamental breakthrough in understanding dielectric contributions of domain walls at THz frequencies. It also demonstrates that THz probing can be used to read domain wall dielectric switching.
    • G-Codes, self-dual G-Codes and reversible G-Codes over the Ring Bj,k

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; Sahinkaya, Serap; Tarsus University; University of Chester (Springer, 2021-05-03)
      In this work, we study a new family of rings, Bj,k, whose base field is the finite field Fpr . We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study G-codes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over Bj,k to a code over Bl,m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2j+k-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi-G codes, which are the images of G-codes under the Gray map, are also Gs-codes for some s.
    • Enhanced design of an offgrid PV-battery-methanation hybrid energy system for power/gas supply

      Xu, x; Hu, W; Cao, D; Liu, W; Huang, Q; Hu, Y; Chen, Z; University of ESTC; Utrecht University; University of Chester; Aalborg University
      Extensive studies have been carried out on various hybrid energy systems (HESs) for providing electricity to off-grid areas. However, a standalone HES that is capable of providing power and gas, has been less studied. In this paper, a standalone Photovoltaic (PV)-battery-methanation HES is proposed to provide adequate, reliable and cost-effective electricity and gas to the local consumers. Identifying a potential solution to maximize the reliability of the system, asked by consumers, and to minimize costs required by the investors is challenging. Bi-level programming is adopted in this study to tackle the pre-mentioned issue. In the outer layer, an optimal design is obtained by means of particle swarm optimization. In the inner layer, an optimal operation strategy is found under the optimal design of the outer layer using sequential quadratic programming. The results indicate that 1) The bi-level programming used in this study can find the optimal solution; 2) The proposed HES is proved to be able to supply power and gas simultaneously. 3) Compared with the right most and leftmost points on Pareto set, the total costs are reduced by 17.77% and 2.16%.
    • 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.
    • Numerical methods for deterministic and stochastic fractional partial differential equations

      Yan, Yubin; Khan, Monzorul (University of Chester, 2020-03)
      In this thesis we will explore the numerical methods for solving deterministic and stochastic space and time fractional partial differential equations. Firstly we consider Fourier spectral methods for solving some linear stochastic space fractional partial differential equations perturbed by space-time white noises in one dimensional case. 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. Secondly we consider Fourier spectral methods for solving stochastic space fractional partial differential equation driven by special additive noises in one dimensional case. 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 appropriate approximations in the space direction. The approximated stochastic space fractional partial differential equation is then solved by using Fourier spectral methods. Thirdly, we will consider the discontinuous Galerkin time stepping methods for solving the linear space fractional partial differential equations. The space fractional derivatives are defined by using Riesz fractional derivative. The space variable is discretized by means of a Galerkin finite element method and the time variable is discretized by the discontinous Galerkin method. The approximate solution will be sought as a piecewise polynomial function in t of degree at most q−1, q ≥ 1, which is not necessarily continuous at the nodes of the defining partition. The error estimates in the fully discrete case are obtained and the numerical examples are given. Finally, we consider error estimates for the modified L1 scheme for solving time fractional partial differential equation. Jin et al. (2016, An analysis of the L1 scheme for the subdiffifusion equation with nonsmooth data, IMA J. of Number. Anal., 36, 197-221) ii established the O(k) convergence rate for the L1 scheme for both smooth and nonsmooth initial data. We introduce a modified L1 scheme and prove that the convergence rate is O(k2−α=), 0 < α < 1 for both smooth and nonsmooth initial data. We first write the time fractional partial differential equations as a Volterra integral equation which is then approximated by using the convolution quadrature with some special generating functions. A Laplace transform method is used to prove the error estimates for the homogeneous time fractional partial differential equation for both smooth and nonsmooth data. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
    • 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.
    • The multi-dimensional Stochastic Stefan Financial Model for a portfolio of assets

      Antonopoulou, Dimitra; Bitsaki, Marina; Karali, Georgia; University of Chester; University of Crete
      The financial model proposed in this work involves the liquidation process of a portfolio of n assets through sell or (and) buy orders placed, in a logarithmic scale, at a (vectorial) price with volatility. We present the rigorous mathematical formulation of this model in a financial setting resulting to an n-dimensional outer parabolic Stefan problem with noise. The moving boundary encloses the areas of zero trading, the so-called solid phase. We will focus on a case of financial interest when one or more markets are considered. In particular, our aim is to estimate for a short time period the areas of zero trading, and their diameter which approximates the minimum of the n spreads of the portfolio assets for orders from the n limit order books of each asset respectively. In dimensions n = 3, and for zero volatility, this problem stands as a mean field model for Ostwald ripening, and has been proposed and analyzed by Niethammer in [25], and in [7] in a more general setting. There in, when the initial moving boundary consists of well separated spheres, a first order approximation system of odes had been rigorously derived for the dynamics of the interfaces and the asymptotic pro le of the solution. In our financial case, we propose a spherical moving boundaries approach where the zero trading area consists of a union of spherical domains centered at portfolios various prices, while each sphere may correspond to a different market; the relevant radii represent the half of the minimum spread. We apply It^o calculus and provide second order formal asymptotics for the stochastic version dynamics, written as a system of stochastic differential equations for the radii evolution in time. A second order approximation seems to disconnect the financial model from the large diffusion assumption for the trading density. Moreover, we solve the approximating systems numerically.
    • The United Kingdom Ministry of Defence and the European Union's electrical and electronic equipment directives

      Powell-Turner, Julieanna; Antill, Peter; Fisher, Richard; Cranfield University
      The growth of the generation of Electrical and Electronic Equipment (EEE), and the use of hazardous substances in the production of these items, has required legislation to minimise the harm to the environment that their existing use, ultimate disposal and continued growth of the sector may pose. The European Union (EU) started to tackle this problem with the passing of two Directives in 2002, which focused on restricting the use of hazardous substances (RoHS - 2002/95/EC) and organising the recycling or disposal of discarded electronic and electrical equipment (WEEE - 2002/96/EC). These Directives have been recently recast and their scope widened; however, one exception to them remains items specifically designed for defence and military purposes. This paper looks at how and why these European Directives were passed, the impact they have had on defence in the United Kingdom (UK) up to the present moment, what impact the further extension of those directives might have on UK defence policy and how the UK Ministry of Defence (MOD) has begun to prepare for any extension, including the use of alternative products from the commercial market, and substituting less harmful materials. The paper reviews the information available to carry out future decision making and what level of decision making it can support. Where the data is insufficient, it makes recommendations on actions to take for improvement.
    • Will Future Resource Demand Cause Significant and Unpredictable Dislocations for the UK Ministry of Defence?

      Antill, Peter; Powell-Turner, Julieanna; Cranfield University
      This paper focuses on the drivers which may affect future trends in material availability for defence, in particular, the availability of rare earth elements (REE). These drivers include resource concentration, tighter regulatory policy and its enforcement, export policies, their use in economic statecraft, increases in domestic demand, promoting greater efficiency in resource use, efforts to mitigate resource depletion and more efficient resource extraction while reducing its associated environmental impact. It looks at the effect these factors might have on global systems and supply chains, the impact on material insecurity and how this may exacerbate the issue of their use in UK military equipment. It finds that these drivers are likely to have an increasing impact on material availability (if measures are not taken to mitigate them), which will have consequences for the provision of military capability by the UK.
    • Talos: a prototype Intrusion Detection and Prevention system for profiling ransomware behaviour

      Wood, Ashley; Eze, Thaddeus; Speakman, Lee; University of Chester (Academic Conferences International, 2021-06-24)
      Abstract: In this paper, we profile the behaviour and functionality of multiple recent variants of WannaCry and CrySiS/Dharma, through static and dynamic malware analysis. We then analyse and detail the commonly occurring behavioural features of ransomware. These features are utilised to develop a prototype Intrusion Detection and Prevention System (IDPS) named Talos, which comprises of several detection mechanisms/components. Benchmarking is later performed to test and validate the performance of the proposed Talos IDPS system and the results discussed in detail. It is established that the Talos system can successfully detect all ransomware variants tested, in an average of 1.7 seconds and instigate remedial action in a timely manner following first detection. The paper concludes with a summarisation of our main findings and discussion of potential future works which may be carried out to allow the effective detection and prevention of ransomware on systems and networks.
    • Computational simulation of the damage response for machining long fibre reinforced plastic (LFRP) composite parts: A review

      Wang, Xiaonan; Wang, Fuji; Gu, Tianyu; Jia, Zhenyuan; Shi, Yu; Dalian University of Technology; University of Chester
      Long fibre reinforced plastics (LFRPs) possess excellent mechanical properties and are widely used in the aerospace, transportation and energy sectors. However, their anisotropic and inhomogeneous characteristics as well as their low thermal conductivity and specific heat capacity make them prone to subsurface damage, delamination and thermal damage during the machining process, which seriously reduces the bearing capacity and shortens the service life of the components. To improve the processing quality of composites, finite element (FE) models were developed to investigate the material removal mechanism and to analyse the influence of the processing parameters on the damage. A review of current studies on composite processing modelling could significantly help researchers to understand failure initiation and development during machining and thus inspire scholars to develop new models with high prediction accuracy and computational efficiency as well as a wide range of applications. To this aim, this review paper summarises the development of LFRP machining simulations reported in the literature and the factors that can be considered in model improvement. Specifically, the existing numerical models that simulate the mechanical and thermal behaviours of LFRPs and LFRP-metal stacks in orthogonal cutting, drilling and milling are analysed. The material models used to characterise the constituent phases of the LFRP parts are reviewed. The mechanism of material removal and the damage responses during the machining of LFRP laminates under different tool geometries and processing parameters are discussed. In addition, novel and objective evaluations that concern the current simulation studies are conducted to summarise their advantages. Aspects that could be improved are further detailed, to provide suggestions for future research relating to the simulation of LFRP machining.
    • Numerical approximation of the Stochastic Cahn-Hilliard Equation near the Sharp Interface Limit

      Antonopoulou, Dimitra; Banas, Lubomir; Nurnberg, Robert; Prohl, Andreas; University of Chester; University of Bielefeld; Imperial College London; University of Tuebingen
      Abstract. We consider the stochastic Cahn-Hilliard equation with additive noise term that scales with the interfacial width parameter ε. We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where ε only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For γ sufficiently large, convergence in probability of iterates towards the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp-interface limit ε → 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ γ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins-Sekerka problem. The computational results indicate that the limit for γ ≥ 1 is the deterministic problem, and for γ = 0 we obtain agreement with a (new) stochastic version of the Mullins-Sekerka problem.
    • Ultrafast Electric Field-induced Phase Transition in Bulk Bi0.5Na0.5TiO3 under High Intensity Terahertz Irradiation

      Yang, Bin; Zhang, Man; McKinnon, Ruth A.; Viola, Giuseppe; Zhang, Dou; Reece, Michael J.; Abrahams, Isaac; Yan, Haixue; University of Chester; Queen Mary University of London; Central South University
      Ultrafast polarization switching is being considered for the next generation of ferroelectric based devices. Recently, the dynamics of the field-induced transitions associated with this switching have been difficult to explore, due to technological limitations. The advent of terahertz (THz) technology has now allowed for the study of these dynamic processes on the picosecond (ps) scale. In this paper, intense terahertz (THz) pulses were used as a high-frequency electric field to investigate ultrafast switching in the relaxor ferroelectric, Bi0.5Na0.5TiO3. Transient atomic-scale responses, which were evident as changes in reflectivity, were captured by THz probing. The high energy THz pulses induce an increase in reflectivity, associated with an ultrafast field-induced phase transition from a weakly polar phase (Cc) to a strongly polar phase (R3c) within 20 ps at 200 K. This phase transition was confirmed using X-ray powder diffraction and by electrical measurements which showed a decrease in the frequency dispersion of relative permittivity at low frequencies.
    • Design, Synthesis and Evaluation of New Bioactive Oxadiazole Derivatives as Anticancer Agents Targeting Bcl-2

      Hamdy, Rania; Elseginy, Samia; Ziedan, Noha; El-Sadek, Mohamed; Lashin, El-Said; Jones, Arwyn T; Westwell, Andrew D; University of Chester; Cardiff University; Zagazig University; Bristol University; University of Sharjah
      A series of 2-(1H-indol-3-yl)-5-substituted-1,3,4-oxadiazoles, 4a–m, were designed, synthesized and tested in vitro as potential pro-apoptotic Bcl-2 inhibitory anticancer agents based on our previously reported hit compounds. Synthesis of the target 1,3,4-oxadiazoles was readily accomplished through a cyclization reaction of indole carboxylic acid hydrazide 2 with substituted carboxylic acid derivatives 3a–m in the presence of phosphorus oxychloride. New compounds 4a–m showed a range of IC50 values concentrated in the low micromolar range selectively in Bcl-2 positive human cancer cell lines. The most potent candidate 4-trifluoromethyl substituted analogue 4j showed selective IC50 values of 0.52–0.88 μM against Bcl-2 expressing cell lines with no inhibitory effects in the Bcl-2 negative cell line. Moreover, 4j showed binding that was two-fold more potent than the positive control gossypol in the Bcl-2 ELISA binding affinity assay. Molecular modeling studies helped to further rationalize anti-apoptotic Bcl-2 binding and identified compound 4j as a candidate with drug-like properties for further investigation as a selective Bcl-2 inhibitory anticancer agent.
    • Entropy-driven cell decision-making predicts "fluid-to-solid" transition in multicellular systems

      Kavallaris, Nikos; Barua, Arnab; Syga, Simon; Mascheroni, Pietro; Meyer-Hermann, Michael; Deutsch, Andreas; Hatzikirou, Haralampos; University of Chester; Helmholtz Centre for Infection Research; Technische Univesität Dresden; Technische Universität Braunschweig; Khalifa University
      Cellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, with or without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatio-temporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelial-mesenchymal transition (EMT) and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy following the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis. In turn, we study the impact of the LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatiotemporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the "solid" tissue phase and its relation with the parameters of the LEUP-driven cell decisions.
    • 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.
    • A promising laser nitriding method for the design of next generation orthopaedic implants: Cytotoxicity and antibacterial performance of titanium nitride (TiN) wear nano-particles, and enhanced wear properties of laser-nitrided Ti6Al4V surfaces

      Chan, Chi Wai; Quinn, James; Hussain, Issam; Carson, Louise; Smith, Graham; Lee, Seunghwan; Queen's University Belfast; University of Lincoln; University of Chester; Technical University of Denmark
      In this study, fibre laser nitriding in open air was applied to the Ti6Al4V alloy in order to improve the wear resistance, thus minimising the generation of wear debris from the surfaces for load-bearing applications. The recent technological advancement to perform the laser nitriding process in open air allows the opportunity to surface-harden any curved and/or specific areas in the hip implants. The laser nitriding process was modulated between the pulsed mode and continuous wave (CW) mode by varying the duty cycle between 60% (pulsed) and 100% (CW). Our experimental investigations were divided into two stages in sequential order: Firstly, to create crack-free, homogenous and golden laser-nitrided surfaces by the proper selection of duty cycle. Secondly, it was to analyse the properties (both physical and chemical) of the wear debris as well as to evaluate their cytotoxicity and antibacterial performance. The laser-nitrided surfaces were characterised and tested using a variety of techniques, incl. optical microscopy, SEM-EDX, XRD, surface roughness and Vickers hardness measurements, as well as tribological tests (i.e. ball-on-disk wear tests and DLS). The wear debris from the laser-nitrided surfaces (collected in the wear tests) were analysed using TEM, XPS and SEM-EDX. Their toxicity was evaluated using in-vitro cell culture with macrophages at two time points (24 h and 48 h). The antibacterial performance was tested in vitro against two of the most commonly implicated pathogens in orthopaedic infection, namely Staphylococcus aureus and Escherichia coli for 24 h. Our findings indicated that the wear resistance of the surfaces after laser nitriding was significantly improved and the amount of wear debris generated was also significantly reduced. The wear particles from the laser-nitrided surfaces were in the nano-sized scale range (0.01 µm to 0.04 µm or 10 nm to 40 nm). They were found to be less toxic towards RAW264.7 macrophages, yet display antimicrobial properties against Staphylococcus aureus, when compared with the larger particles (1.5 µm in size) from the untreated surfaces. It is envisioned that successful fabrication of the non-toxic and highly wear-resistant TiN layer in Ti6Al4V using the open-air laser nitriding technique can enable progress towards the development of metal-on-metal (MoM) hip implants fully made of Ti-based alloys