• Obesity and the Dysregulation of Fatty Acid Metabolism: Implications for Healthy Aging

      Morgan, Amy; Mooney, Kathleen M.; Mc Auley, Mark T.; University of Chester; Edge Hill University (Taylor & Francis, 2016-10-17)
      The population of the world is aging. In 2010, an estimated 524 million people were aged 65 years or older presenting eight percent of the global population. By 2050, this number is expected to nearly triple to approximately 1.5 billion, 16 percent of the world’s population. Although people are living longer, the quality of their lives are often compromised due to ill-health. Areas covered. Of the conditions which compromise health as we age, obesity is at the forefront. Over half of the global older population were overweight or obese in 2010, significantly increasing the risk of a range of metabolic diseases. Although, it is well recognised excessive calorie intake is a fundamental driver of adipose tissue dysfunction, the relationship between obesity; intrinsic aging; and fat metabolism is less understood. In this review we discuss the intersection between obesity, aging and the factors which contribute to the dysregulation of whole-body fat metabolism. Expert Commentary. Being obese disrupts an array of physiological systems and there is significant crosstalk among these. Moreover it is imperative to acknowledge the contribution intrinsic aging makes to the dysregulation of these systems and the onset of disease.
    • On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics

      Kavallaris, Nikos I.; Lankeit, Johannes; Winkler, Michael; University of Chester; Paderborn University (SIAM, 2017-03-28)
      We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega |\nabla u|^2 \] in bounded domains $\Om\sub\R^n$ which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global.
    • On Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations

      Baker, Christopher T. H.; Buckwar, Evelyn; University College Chester (World Scientific Publishing, 2009-05-0)
    • On hereditary reducibility of 2-monomial matrices over commutative rings

      Bondarenko, Vitaliy M.; Gildea, Joe; Tylyshchak, Alexander; Yurchenko, Natalia; Institute of Mathematic, Kyiv; University of Chester; Uzhgorod National University (Taras Shevchenko National University of Luhansk, 2019)
      A 2-monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{n-k}\end{smallmatrix}\right)$, $0<k<n$, where $t$ is a non-invertible element of $R$, $\Phi$ the compa\-nion matrix to $\lambda^n-1$ and $I_k$ the identity $k\times k$-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility.
    • On integral equation formulation of a class of evolutionary equations with time-lag

      Baker, Christopher T. H.; Lumb, Patricia M. (Rocky Mountain Mathematics Consortium, 2006)
    • On some aspects of casual and neutral equations used in mathematical modelling

      Baker, Christopher T. H.; Bocharov, Gennady; Parmuzin, Evgeny I.; Rihan, F. A. R.; University of Chester (University of Chester, 2007)
      The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) roles for well-defined ad-joints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.
    • On the behavior of the solutions for linear autonomous mixed type difference equation

      Yan, Yubin; Yenicerioglu, Ali Fuat; Pinelas, Sandra; University of Chester; Kocaeli University, Turkey; RUDN University, Russia (Springer Link, 2019-07-30)
      A class of linear autonomous mixed type difference equations is considered, and some new results on the asymptotic behavior and the stability are given, via a positive root of the corresponding characteristic equation.
    • On the decay of the elements of inverse triangular Toeplitz matrices

      Ford, Neville J.; Savostyanov, Dmitry V.; Zamarashkin, Nickolai L.; University of Chester ; University of Chester ; Institute of Numerical Mathematics, Russian Academy of Sciences (Society for Industrial and Applied Mathematics, 2014-10-28)
      We consider half–infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of p–norms. The results add to the classical results of Jaffard and Vecchio, and are illustrated by numerical examples.
    • On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the half-line

      Antonopoulou, Dimitra; Kamvissis, Spyridon; Department of Mathematics, University of Chester, UK(D.A) and Department of Mathematics and Applied Mathematics, University of Crete, Greece (S.K) (IOPSCIENCE Published jointly with the London Mathematical Society, 2015-07-24)
      Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data su ces to make the problem well-posed but the Fokas method also requires knowledge of the values of Neumann data. The study of the Dirichlet to Neumann map is thus necessary before the application of the `Fokas transform'. In this paper, we provide a rigorous study of this map for a large class of decaying Dirichlet data. We show that the Neumann data are also su ciently decaying and that, hence, the Fokas method can be applied.
    • On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system

      Kavallaris, Nikos I.; Suzuki, Takashi; University of Chester; Osaka University (London Mathematical Society, 2017-03-21)
      The purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a Gierer-Meinhardt model. Shadow systems are intended to work as an intermediate step between single equations and reaction-diffusion systems. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics will be investigated. We mainly focus on the derivation of blow-up results for this non-local equation which can be seen as instability patterns of the shadow system. In particular, a {\it diffusion driven instability (DDI)}, or {\it Turing instability}, in the neighbourhood of a constant stationary solution, which it is destabilised via diffusion-driven blow-up, is obtained. The latter actually indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns.
    • On the quenching behaviour of a semilinear wave equation modelling MEMS technology

      Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.; Tzanetis, Dimitrios E.; University of Chester ; Heriot-Watt University ; University of Aegean ; National Technical University of Athens (American Institute of Mathematical Sciences, 2014-10-01)
    • On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

      Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.; University of Chester; Heriot-Watt University; University of Aegean (Elsevier, 2016-02-28)
      We consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.
    • On the study of oil paint adhesion on optically transparent glass: Conservation of reverse paintings on glass

      Bayle, M.; Waugh, David G.; Colston, Belinda J.; Lawrence, Jonathan; University of Chester (Elsevier, 2015-12-01)
      Reverse painting on glass is a technique which consists of applying a cold paint layer on the reverse-side of glass. The main challenge facing these artworks is the fragile adhesion of the pictorial layer – a simple movement can modify the appearance of the painting. This paper details a study into the adhesion parameters of pigments on glass and the comparison between different pigments. The relationships between the binder (linseed oil) with pigments and the glass with or without the use of an adhesive are studied. Physical analyses by surface characterisation have been carried out to better understand the influence of the pigment. The use of a sessile drop device, optical microscopy, scanning electron microscopy (SEM), a surface 3D profiler and a pencil hardness scratch tester were necessary to establish a comparison of the pictorial layer adhesion. A comparison of the effect of two adhesives; namely ox gall and gum arabic, has shown that the adhesion is not only linked to the physical parameters but that possible chemical reactions can influence the results. Finally, a treatment based on humidity-extreme storage has shown the weakness of some pictorial layers.
    • Online conductivity calibration methods for EIT gas/oil in water flow measurement

      Jia, Jiabin; Wang, Mi; Faraj, Yousef; Wang, Qiang; University of Chester; University of Leeds; University of Edinburgh (Elsevier, 2015-07-02)
      Electrical Impedance Tomography (EIT) is a fast imaging technique displaying the electrical conductivity contrast of multiphase flow. It is increasingly utilised for industrial process measurement and control. In principle, EIT has to obtain the prior information of homogenous continuous phase in terms of conductivity as a reference benchmark. This reference significantly influences the quality of subsequent multiphase flow measurement. During dynamic industrial process, the conductivity of continuous phase varies due to the effects from the changes of ambient and fluid temperature, ionic concentration, and internal energy conversion in fluid. It is not practical to stop industrial process frequently and measure the conductivity of continuous phase for taking the EIT reference. If without monitoring conductivity of continuous phase, EIT cannot present accurate and useful measurement results. To online calibrate the electrical conductivity of continuous phase and eliminate drift error of EIT measurement, two methods are discussed in this paper. Based on the linear approximation between fluid temperature and conductivity, the first method monitors fluid temperature and indirectly calibrates conductivity. In the second method, a novel conductivity cell is designed. It consists of a gravitational separation chamber with refreshing bypass and grounded shielding plate. The conductivity of continuous phase is directly sensed by the conductivity cell and fed to EIT system for online calibration. Both static and dynamic experiments were conducted to demonstrate the function and accuracy the conductivity cell.
    • Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions

      Liu, Fang; Liang, Zongqi; Yan, Yubin; Luliang University; Jimei University; University of Chester (Elsevier, 2018-12-17)
      We consider the optimal convergence rates of the semidiscrete finite element approximations for solving linear space-fractional partial differential equations by using the regularity results for the fractional elliptic problems obtained recently by Jin et al. \cite{jinlazpasrun} and Ervin et al. \cite{ervheuroo}. The error estimates are proved by using two approaches. One approach is to apply the duality argument in Johnson \cite{joh} for the heat equation to consider the error estimates for the linear space-fractional partial differential equations. This argument allows us to obtain the optimal convergence rates under the minimal regularity assumptions for the solution. Another approach is to use the approximate solution operators of the corresponding fractional elliptic problems. This argument can be extended to consider more general linear space-fractional partial differential equations. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
    • Optimisation and management of energy generated by a multifunctional MFC-integrated composite chassis for rail vehicles

      Liu, Yiding; Du, Sijun; Micallef, Christopher; Jia, Yu; Shi, Yu; Hughes, Darren; University of Warwick; University of California at Berkeley; Aston University; University of Chester
      With the advancing trend towards lighter and faster rail transport, there is an increasing interest in integrating composite and advanced multifunctional materials in order to infuse smart sensing and monitoring, energy harvesting and wireless capabilities within the otherwise purely mechanical rail structures and the infrastructure. This paper presents a holistic multiphysics numerical study, across both mechanical and electrical domains, that describes an innovative technique of harvesting energy from a piezoelectric micro fiber composites (MFC) built-in composite rail chassis structure. Representative environmental vibration data measured from a rail cabin have been critically leveraged here to help predict the actual vibratory and power output behaviour under service. Time domain mean stress distribution data from the Finite Element simulation were used to predict the raw AC voltage output of the MFCs. Conditioned power output was then calculated using circuit simulation of several state-of-the-art power conditioning circuits. A peak instantaneous rectified power of 181.9 mW was obtained when eight-stage Synchronised Switch Harvesting Capacitors (SSHC) from eight embedded MFCs were located. The results showed that the harvested energy could be sufficient to sustain a self-powered structural health monitoring system with wireless communication capabilities. This study serves as a theoretical foundation of scavenging for vibrational power from the ambient state in a rail environment as well as to pointing to design principles to develop regenerative and power neutral smart vehicles.
    • Optimization of anti-wear and anti-bacterial properties of beta TiNb alloy via controlling duty cycle in open-air laser nitriding

      Chang, Xianwen; Smith, Graham; Quinn, James; Carson, Louise; Chan, Chi-Wai; Lee, Seunghwan; Technical University of Denmark (Chang, Lee), University of Chester (Smith), Queens University Belfast (Quinn, Chan) (Elsevier, 2020-07-09)
      A multifunctional beta TiNb surface, featuring wear-resistant and antibacterial properties, was successfully created by means of open-air fibre laser nitriding. Beta TiNb alloy was selected in this study as it has low Young’s modulus, is highly biocompatible, and thus can be a promising prosthetic joint material. It is, however, necessary to overcome intrinsically weak mechanical properties and poor wear resistance of beta TiNb in order to cover the range of applications to loadbearing and/or shearing parts. To this end, open-air laser nitriding technique was employed. A control of single processing parameter, namely duty cycle (between 5% and 100%), led to substantially different structural and functional properties of the processed beta TiNb surfaces as analyzed by an array of analytical tools. The TiNb samples nitrided at the DC condition of 60% showed a most enhanced performance in terms of improving surface hardness, anti-friction, antiwear and anti-bacterial properties in comparison with other conditions. These findings are expected to be highly important and useful when TiNb alloys are considered as materials for hip/knee articular joint implants
    • Orthogonality for a class of generalised Jacobi polynomial $P^{\alpha,\beta}_{\nu}(x)$

      Ford, Neville J.; Moayyed, H.; Rodrigues, M. M.; University of Chester, University of Aveiro, University of Aveiro (Ele-Math, 2018-08-06)
      This work considers g-Jacobi polynomials, a fractional generalisation of the classical Jacobi polynomials. We discuss the polynomials and compare some of their properties to the classical case. The main result of the paper is to show that one can derive an orthogonality property for a sub-class of g-Jacobi polynomials $P^{\alpha,\beta}_{\nu}(x)$ The paper concludes with an application in modelling of ophthalmic surfaces.
    • Overcurrent relays coordination optimisation methods in distribution systems for microgrids: a review

      Abeid, S; Hu, Yanting; University of Chester
      Electric power networks connected with multiple distributed generations (microgrids) require adequate protection coordination. In this paper, the overcurrent relay coordination concept in distribution system has been presented with details. In this available literature, the previous works on optimisation methods utilised for the coordination of over current relays; classification has been made based on the optimisation techniques, non-standard characteristics, new constraints that have been proposed for optimal coordination and dual setting protection schemes. Then a comprehensive review has been done on optimisation techniques including the conventional methods, heuristic and hybrid methods and the relevant issues have been addressed.
    • An overview of self-adaptive technologies within virtual reality training

      Vaughan, Neil; Gabrys, Bogdan; Dubey, Venketesh; University of Chester
      This overview presents the current state-of-the-art of self-adaptive technologies within virtual reality (VR) training. Virtual reality training and assessment is increasingly used for five key areas: medical, industrial & commercial training, serious games, rehabilitation and remote training such as Massive Open Online Courses (MOOCs). Adaptation can be applied to five core technologies of VR including haptic devices, stereo graphics, adaptive content, assessment and autonomous agents. Automation of VR training can contribute to automation of actual procedures including remote and robotic assisted surgery which reduces injury and improves accuracy of the procedure. Automated haptic interaction can enable tele-presence and virtual artefact tactile interaction from either remote or simulated environments. Automation, machine learning and data driven features play an important role in providing trainee-specific individual adaptive training content. Data from trainee assessment can form an input to autonomous systems for customised training and automated difficulty levels to match individual requirements. Self-adaptive technology has been developed previously within individual technologies of VR training. One of the conclusions of this research is that while it does not exist, an enhanced portable framework is needed and it would be beneficial to combine automation of core technologies, producing a reusable automation framework for VR training.