Faculty of Science and Engineering
Based at Thornton Science Park, the new Faculty of Science and Engineering is located in a major research and innovation hub for the North West which is only a 20minute bus trip from the main Chester Campus. The Faculty offers degrees in engineering and science disciplines using a strongly interdisciplinary teaching philosophy.
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SpaceTime Discontinuous Galerkin Methods for the '\eps'dependent Stochastic AllenCahn Equation with mild noise(Oxford University Press, 2019)We consider the $\eps$dependent stochastic AllenCahn equation with mild space time noise posed on a bounded domain of R^2. The positive parameter $\eps$ is a measure for the inner layers width that are generated during evolution. This equation, when the noise depends only on time, has been proposed by Funaki in [15]. The noise although smooth becomes white on the sharp interface limit as $\eps$ tends to zero. We construct a nonlinear dG scheme with spacetime finite elements of general type which are discontinuous in time. Existence of a unique discrete solution is proven by application of Brouwer's Theorem. We first derive abstract error estimates and then for the case of piecewise polynomial finite elements we prove an error in expectation of optimal order. All the appearing constants are estimated in terms of the parameter $\eps$. Finally, we present a linear approximation of the nonlinear scheme for which we prove existence of solution and optimal error in expectation in piecewise linear finite element spaces. The novelty of this work is based on the use of a finite element formulation in space and in time in 2+1dimensional subdomains for a nonlinear parabolic problem. In addition, this problem involves noise. These type of schemes avoid any RungeKutta type discretization for the evolutionary variable and seem to be very effective when applied to equations of such a difficulty.

Numerical analysis of a twoparameter fractional telegraph equation(Elsevier, 20130926)In this paper we consider the twoparameter fractional telegraph equation of the form $$\, ^CD_{t_0^+}^{\alpha+1} u(t,x) + \, ^CD_{x_0^+}^{\beta+1} u (t,x) \, ^CD_{t_0^+}^{\alpha}u (t,x)u(t,x)=0.$$ Here $\, ^CD_{t_0^+}^{\alpha}$, $\, ^CD_{t_0^+}^{\alpha+1}$, $\, ^CD_{x_0^+}^{\beta+1}$ are operators of the Caputotype fractional derivative, where $0\leq \alpha < 1$ and $0 \leq \beta < 1$. The existence and uniqueness of the equations are proved by using the Banach fixed point theorem. A numerical method is introduced to solve this fractional telegraph equation and stability conditions for the numerical method are obtained. Numerical examples are given in the final section of the paper.

Stabilizing a mathematical model of plant species interaction(Elsevier, 20110903)In this paper, we will consider how to stabilize a mathematical model of plant species interaction which is modelled by using LotkaVolterra system. We first identify the unstable steady states of the system, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. We further stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas.

Stability of a numerical method for a fractional telegraph equation(De Gruyter, 201203)In this paper, we introduce a numerical method for solving the timespace fractional telegraph equations. The numerical method is based on a quadrature formula approach and a stability condition for the numerical method is obtained. Two numerical examples are given and the stability regions are plotted.

Nanodiamond based surface modified screenprinted electrodes for the simultaneous voltammetric determination of dopamine and uric acid.(20190222)The electroanalytical detection of the neurotransmitter dopamine (DA) in the presence of uric acid (UA) is explored for the first time using commercially procured nanodiamonds (NDs). These are electrically wired via surface modification upon screenprinted graphite macroelectrodes (SPEs). The surface coverage of the NDs on the SPEs was explored in order to optimize electroanalytical outputs to result in wellresolved signals and in low limits of detection. The (electro)analytical outputs are observed to be more sensitive than those achieved at bare (unmodified) SPEs. Such responses, previously reported in the academic literature have been reported to be electrocatalytic and have been previously attributed to the presence of surface sp carbon and oxygenated species on the surface of the NDs. However, XPS analysis reveals the commercial NDs to be solely composed of nonconductive sp carbon. The low/negligible electroconductivity of the NDs was further confirmed when ND paste electrodes were fabricated and found to exhibit no electrochemical activity. The electroanalytical enhancement, when using NDs electronically wired upon SPEs, is attributed not to the NDs themselves being electrocatalytic, as reported previously, but rather changes in mass transport where the inert NDs block the underlying electroactive SPEs and create a random array of graphite microelectrodes. The electrode was applied to simultaneous sensing of DA and UA at pH 5.5. Figures of merit include (a) low working potentials of around 0.27 and 0.35 V (vs. Ag/AgCl); and (b) detection limits of 5.7 × 10 and 8.9 × 10 M for DA and UA, respectively. Graphical abstract The electroanalytical enhancement of screenprinted electrodes modified with inert/nonconductive nanodiamonds is due to a change in mass transfer where the inert nanodiamonds facilitate the production of a random microelectrode array.

Adapting Jake Knapp’s Design Sprint Approach for AR/VR Applications in Digital Heritage(Springer Nature, 2019)Modern digital devices offer huge potential for the delivery of engaging heritage experiences to visitors, offering a better visitor experience, higher visitor numbers, and opportunities for increased tourism income. However, all software development entails risk, including the risk of developing a product which few will want, or be able, to use. Identifying user experience priorities and problems at an early stage is therefore extremely important. This chapter describes work in progress on a shortened version of Jake Knapp’s Design Sprint approach, and its application to designing VR/AR solutions for a specific heritage case study.

The Interplay Between Cholesterol Metabolism and Intrinsic Ageing.(2018)The last few decades have witnessed remarkable progress in our understanding of ageing. From an evolutionary standpoint it is generally accepted that ageing is a nonadaptive process which is underscored by a decrease in the force of natural selection with time. From a mechanistic perspective ageing is characterized by a wide variety of cellular mechanisms, including processes such as cellular senescence, telomere attrition, oxidative damage, molecular chaperone activity, and the regulation of biochemical pathways by sirtuins. These biological findings have been accompanied by an unrelenting rise in both life expectancy and the number of older people globally. However, despite age being recognized demographically as a risk factor for healthspan, the processes associated with ageing are routinely overlooked in disease mechanisms. Thus, a central goal of biogerontology is to understand how diseases such as cardiovascular disease (CVD) are shaped by ageing. This challenge cannot be ignored because CVD is the main cause of morbidity in older people. A worthwhile way to examine how ageing intersects with CVD is to consider the effects ageing has on cholesterol metabolism, because dysregualted cholesterol metabolism is the key factor which underpins the pathology of CVD. The aim of this chapter is to outline a hypothesis which accounts for how ageing intersects with intracellular cholesterol metabolism. Moreover, we discuss the implications of this relationship for the onset of disease in the 'oldest old' (individuals ≥85 years of age). We conclude the chapter by discussing the important role mathematical modelling has to play in improving our understanding of cholesterol metabolism and ageing.

Investigation of size, concentration and particle shapes in hydraulic systems using an inline CMOS image matrix sensor(University of ChesterWrexham Glyndŵr UniversityUniversity of Chester, 20180921)The theoretical and experimental investigation of the novel inline 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.

On hereditary reducibility of 2monomial matrices over commutative rings(Taras Shevchenko National University of Luhansk, 2019)A 2monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{nk}\end{smallmatrix}\right)$, $0<k<n$, where $t$ is a noninvertible element of $R$, $\Phi$ the compa\nion matrix to $\lambda^n1$ 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.

Colour Coded Emotion Classification in Mental Health Social Media(BCS, The Chartered Institute for IT, ACM Proceedings, 20180706)This research applies emotion detection to messages from online mental health social media. In particular, this focusses on specialised social media for users to report health or mental health problems. Automatically detecting the emotion in social media can help to rapidly identify any concerning problems which could benefit from intervention aiming to prevent selfharming or suicide. Detecting emotions enables messages to be colour coordinated according to the emotion to enhance the humancomputer interaction. A supervised classification method is applied to a labelled dataset and results presented. A prototype user interface system is developed based on detecting emotion, colour coding the message to display detected emotions to users in realtime.

A high order numerical method for solving nonlinear fractional differential equation with nonuniform meshes(Springer Link, 20190118)We introduce a highorder numerical method for solving nonlinear fractional differential equation with nonuniform meshes. We first transform the fractional nonlinear differential equation into the equivalent Volterra integral equation. Then we approximate the integral by using the quadratic interpolation polynomials. On the first subinterval $[t_{0}, t_{1}]$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{0}, t_{1}, t_{2}$ and in the other subinterval $[t_{j}, t_{j+1}], j=1, 2, \dots N1$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{j1}, t_{j}, t_{j+1}$. A highorder numerical method is obtained. Then we apply this numerical method with the nonuniform meshes with the step size $\tau_{j}= t_{j+1} t_{j}= (j+1) \mu$ where $\mu= \frac{2T}{N (N+1)}$. Numerical results show that this method with the nonuniform meshes has the higher convergence order than the standard numerical methods obtained by using the rectangle and the trapzoid rules with the same nonuniform meshes.

Programmable logic controllers and Direct digital controls in Buildings(201809)The concept of programmable logic controller (PLC) originated over the last century that has revolutionised the industrial sector. In the last few decades PLC in the form of DDC has been commonly used in Building Energy Management Systems (BEMS). The contribution of this work is to analyse PLC/DDC role in the ongoing BEMS advancements in the building sector. Currently DDC are not understood by building design and simulation engineers who assess the controllability of the building in practice. This paper would enhance the understanding of integrating DDC in buildings and influence creation of better modelling and simulation tools for assessing their impact on energy performance in practice.

New SelfDual and Formally SelfDual Codes from Group Ring Constructions(American Institute of Mathematical Sciences, 2019)In this work, we study construction methods for selfdual and formally selfdual codes from group rings, arising from the cyclic group, the dihedral group, the dicyclic group and the semidihedral group. Using these constructions over the rings $_F2 +uF_2$ and $F_4 + uF_4$, we obtain 9 new extremal binary selfdual codes of length 68 and 25 even formally selfdual codes with parameters [72,36,14].

High performing AgNW transparent conducting electrodes with a sheet resistance of 2.5 Ω Sq−1 based upon a rolltoroll compatible postprocessing technique(Royal Society of Chemistry, 20190212)The report of transparent and conducting silver nanowires (AgNWs) that produce remarkable electrical performance, surface planarity and environmental stability is given. This research presents an innovative process that relies on three sequential steps, which are rolltoroll (R2R) compatible; thermal embossing, infrared sintering and plasma treatment. This process leads to the demonstration of a conductive film with a sheet resistance of 2.5Ω/sq and high transmittance, thus demonstrating the highest reported figureofmerit in AgNWs to date (FoM = 933). A further benefit of the process is that the surface roughness is substantially reduced compared to traditional AgNW processing techniques. Finally, consideration of the longterm stability is given by developing an accelerated life test process that simultaneously stresses the applied bias and temperature. Regression line fitting shows that a ∼150times improvement in stability is achieved at ‘normal operational conditions’ when compared to traditionally deposited AgNW films. Xray photoelectron spectroscopy (XPS) is used to understand the root cause of the improvement in longterm stability, which is related to reduced chemcial changes in the AgNWs.

VRIA  A Framework for Immersive Analytics on the Web(ACM, 201905)We report on the design, implementation and evaluation of <VRIA>, a framework for building immersive analytics (IA) solutions inWebbased Virtual Reality (VR), built upon WebVR, AFrame, React and D3. The recent emergence of affordable VR interfaces have reignited the interest of researchers and developers in exploring new, immersive ways to visualize data. In particular, the use of openstandards webbased technologies for implementing VR in a browser facilitates the ubiquitous and platformindependent adoption of IA systems. Moreover, such technologies work in synergy with established visualization libraries, through the HTML document object model (DOM). We discuss highlevel features of <VRIA> and present a preliminary user experience evaluation of one of our usecases.

Bordered Constructions of SelfDual Codes from Group Rings and New Extremal Binary SelfDual Codes(Elsevier, 2019)We introduce a bordered construction over group rings for selfdual codes. We apply the constructions over the binary field and the ring $\F_2+u\F_2$, using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary selfdual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary selfdual codes of length 72. In particular we obtain 41 new binary extremal selfdual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.

Appearance Modeling of Living Human Tissues(Wiley, 2019)The visual fidelity of realistic renderings in Computer Graphics depends fundamentally upon how we model the appearance of objects resulting from the interaction between light and matter reaching the eye. In this paper, we survey the research addressing appearance modeling of living human tissue. Among the many classes of natural materials already researched in Computer Graphics, living human tissues such as blood and skin have recently seen an increase in attention from graphics research. There is already an incipient but substantial body of literature on this topic, but we also lack a structured review as presented here. We introduce a classification for the approaches using the four types of human tissues as classifiers. We show a growing trend of solutions that use first principles from Physics and Biology as fundamental knowledge upon which the models are built. The organic quality of visual results provided by these Biophysical approaches is mainly determined by the optical properties of biophysical components interacting with light. Beyond just picture making, these models can be used in predictive simulations, with the potential for impact in many other areas.

Optimal convergence rates for semidiscrete finite element approximations of linear spacefractional partial differential equations under minimal regularity assumptions(Elsevier, 20181217)We consider the optimal convergence rates of the semidiscrete finite element approximations for solving linear spacefractional 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 spacefractional 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 spacefractional partial differential equations. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Datadriven selection and parameter estimation for DNA methylation mathematical models(Elsevier, 20190110)Epigenetics is coming to the fore as a key process which underpins health. In particular emerging experimental evidence has associated alterations to DNA methylation status with healthspan and aging. Mammalian DNA methylation status is maintained by an intricate array of biochemical and molecular processes. It can be argued changes to these fundamental cellular processes ultimately drive the formation of aberrant DNA methylation patterns, which are a hallmark of diseases, such as cancer, Alzheimer's disease and cardiovascular disease. In recent years mathematical models have been used as e ective tools to help advance our understanding of the dynamics which underpin DNA methylation. In this paper we present linear and nonlinear models which encapsulate the dynamics of the molecular mechanisms which de ne DNA methylation. Applying a recently developed Bayesian algorithm for parameter estimation and model selection, we are able to estimate distributions of parameters which include nominal parameter values. Using limited noisy observations, the method also identifed which methylation model the observations originated from, signaling that our method has practical applications in identifying what models best match the biological data for DNA methylation.