• Oscillatory and stability of a mixed type difference equation with variable coefficients

      Yan, Yubin; Pinelas, Sandra; Ramdani, Nedjem; Yenicerioglu, Ali Fuat; RUDN University; University of Saad Dahleb Blida; Kocaeli University; University of Chester (Inderscience, 2021-08-12)
      The goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients \[ \Delta x(n)=\sum_{i=1}^{\ell}p_{i}(n)x(\tau_{i}(n))+\sum_{j=1}^{m}q_{j}(n)x(\sigma_{i}(n)),\quad n\ge n_{0}, \] where $\tau_{i}(n)$ is the delay term and $\sigma_{j}(n)$ is the advance term and they are positive real sequences for $i=1,\cdots,l$ and $j=1,\cdots,m$, respectively, and $p_{i}(n)$ and $q_{j}(n)$ are real functions. This paper generalise some known results and the examples illustrate the results.
    • Spatial discretization for stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise

      Yan, Yubin; Hoult, James; Wang, Junmei; University of Chester; LuLiang University (MDPI, 2021-08-12)
      Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.
    • Error estimates of a continuous Galerkin time stepping method for subdiffusion problem

      Yan, Yubin; Yan, Yuyuan; Liang, Zongqi; Egwu, Bernard; Jimei University; University of Chester (Springer, 2021-07-29)
      A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time $t$ and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order $O(\tau^{1+ \alpha}), \, \alpha \in (0, 1)$ for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where $\tau$ is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only $O(\tau)$ convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.
    • Multi-metric Evaluation of the Effectiveness of Remote Learning in Mechanical and Industrial Engineering During the COVID-19 Pandemic: Indicators and Guidance for Future Preparedness

      Behera, Amar Kumar; de Sousa, Ricardo Alves; Oleksik, Valentin; Dong, Jingyan; Fritzen, Daniel; University of Chester; University of Aveiro; Lucian Blaga University of Sibiu; North Carolina State University; SATC College (UK Data Service, 2021-07-27)
      This data set contains data collected from 5 universities in 5 countries about the effectiveness of e-learning during the COVID-19 pandemic, specifically tailored to mechanical and industrial engineering students. A survey was administered in May, 2020 at these universities simultaneously, using Google Forms. The survey had 41 questions, including 24 questions on a 5-point Likert scale. The survey questions gathered data on their program of study, year of study, university of enrolment and mode of accessing their online learning content. The Likert scale questions on the survey gathered data on the effectiveness of digital delivery tools, student preferences for remote learning and the success of the digital delivery tools during the pandemic. All students enrolled in modules taught by the authors of this study were encouraged to fill the survey up. Additionally, remaining students in the departments associated with the authors were also encouraged to fill up the form through emails sent on mailing lists. The survey was also advertised on external websites such as survey circle and facebook. Crucial insights have been obtained after analysing this data set that link the student demographic profile (gender, program of study, year of study, university) to their preferences for remote learning and effectiveness of digital delivery tools. This data set can be used for further comparative studies and was useful to get a snapshot of student preferences and e-learning effectiveness during the COVID-19 pandemic, which required the use of e-learning tools on a wider scale than previously and using new modes such as video conferencing that were set up within a short timeframe of a few days or weeks.
    • Group Codes, Composite Group Codes and Constructions of Self-Dual Codes

      Gildea, Joe; Korban, Adrian (University of Chester, 2021-08)
      The main research presented in this thesis is around constructing binary self-dual codes using group rings together with some well-known code construction methods and the study of group codes and composite group codes over different alphabets. Both these families of codes are generated by the elements that come from group rings. A search for binary self-dual codes with new weight enumerators is an ongoing research area in algebraic coding theory. For this reason, we present a generator matrix in which we employ the idea of a bisymmetric matrix with its entries being the block matrices that come from group rings and give the necessary conditions for this generator matrix to produce a self-dual code over a fi nite commutative Frobenius ring. Together with our generator matrix and some well-known code construction methods, we find many binary self-dual codes with parameters [68, 34, 12] that have weight enumerators that were not known in the literature before. There is an extensive literature on the study of different families of codes over different alphabets and speci fically finite fi elds and finite commutative rings. The study of codes over rings opens up a new direction for constructing new binary self-dual codes with a rich automorphism group via the algebraic structure of the rings through the Gray maps associated with them. In this thesis, we introduce a new family of rings, study its algebraic structure and show that each member of this family is a commutative Frobenius ring. Moreover, we study group codes over this new family of rings and show that one can obtain codes with a rich automorphism group via the associated Gray map. We extend a well established isomorphism between group rings and the subring of the n x n matrices and show its applications to algebraic coding theory. Our extension enables one to construct many complex n x n matrices over the ring R that are fully de ned by the elements appearing in the first row. This property allows one to build generator matrices with these complex matrices so that the search field is practical in terms of the computational times. We show how these complex matrices are constructed using group rings, study their properties and present many interesting examples of complex matrices over the ring R. Using our extended isomorphism, we de ne a new family of codes which we call the composite group codes or for simplicity, composite G-codes. We show that these new codes are ideals in the group ring RG and prove that the dual of a composite G-code is also a composite G-code. Moreover, we study generator matrices of the form [In | Ω(v)]; where In is the n x n identity matrix and Ω(v) is the composite matrix that comes from the extended isomorphism mentioned earlier. In particular, we show when such generator matrices produce self-dual codes over finite commutative Frobenius rings. Additionally, together with some generator matrices of the type [In | Ω(v)] and the well-known extension and neighbour methods, we fi nd many new binary self-dual codes with parameters [68, 34, 12]. Lastly in this work, we study composite G-codes over formal power series rings and finite chain rings. We extend many known results on projections and lifts of codes over these alphabets. We also extend some known results on γadic codes over the infi nite ring R∞
    • Layer Dynamics for the one dimensional $\eps$-dependent Cahn-Hilliard / Allen-Cahn Equation

      Antonopoulou, Dimitra; Karali, Georgia; Tzirakis, Konstantinos; University of Chester; University of Crete; IACM/FORTH (Springer, 2021-08-27)
      We study the dynamics of the one-dimensional ε-dependent Cahn-Hilliard / Allen-Cahn equation within a neighborhood of an equilibrium of N transition layers, that in general does not conserve mass. Two different settings are considered which differ in that, for the second, we impose a mass-conservation constraint in place of one of the zero-mass flux boundary conditions at x = 1. Motivated by the study of Carr and Pego on the layered metastable patterns of Allen-Cahn in [10], and by this of Bates and Xun in [5] for the Cahn-Hilliard equation, we implement an N-dimensional, and a mass-conservative N−1-dimensional manifold respectively; therein, a metastable state with N transition layers is approximated. We then determine, for both cases, the essential dynamics of the layers (ode systems with the equations of motion), expressed in terms of local coordinates relative to the manifold used. In particular, we estimate the spectrum of the linearized Cahn-Hilliard / Allen-Cahn operator, and specify wide families of ε-dependent weights δ(ε), µ(ε), acting at each part of the operator, for which the dynamics are stable and rest exponentially small in ε. Our analysis enlightens the role of mass conservation in the classification of the general mixed problem into two main categories where the solution has a profile close to Allen-Cahn, or, when the mass is conserved, close to the Cahn-Hilliard solution.
    • Characterization of microwave and terahertz dielectric properties of single crystal La2Ti2O7 along one single direction

      Zhang, Man; Tang, Zhiyong; Zhang, Hangfeng; Smith, Graham; Jiang, Qinghui; Saunders, Theo; Yang, Bin; Yan, Haixue; Huazhong University of Science and Technology; University of Chester; Queen Mary University of London; Chinese Academy of Sciences (Elsevier, 2021-08-02)
      New generation wireless communication systems require characterisations of dielectric permittivity and loss tangent at microwave and terahertz bands. La2Ti2O7 is a candidate material for microwave application. However, all the reported microwave dielectric data are average value from different directions of a single crystal, which could not reflect its anisotropic nature due to the layered crystal structure. Its dielectric properties at the microwave and terahertz bands in a single crystallographic direction have rarely been reported. In this work, a single crystal ferroelectric La2Ti2O7 was prepared by floating zone method and its dielectric properties were characterized from 1 kHz to 1 THz along one single direction. The decrease in dielectric permittivity with increasing frequency is related to dielectric relaxation from radio frequency to microwave then to terahertz band. The capability of characterizing anisotropic dielectric properties of a single crystal in this work opens the feasibility for its microwave and terahertz applications.
    • Millimeter-Wave Free-Space Dielectric Characterization

      Liu, Xiaoming; Gan, Lu; Yang, Bin; Anhui Normal University; Wuhu CEPREI Information Industry Technology Research Institute; University of Chester (Elsevier, 2021-05-07)
      Millimeter wave technologies have widespread applications, for which dielectric permittivity is a fundamental parameter. The non-resonant free-space measurement techniques for dielectric permittivity using vector network analysis in the millimeter wave range are reviewed. An introductory look at the applications, significance, and properties of dielectric permittivity in the millimeter wave range is addressed first. The principal aspects of free-space millimeter wave measurement methods are then discussed, by assessing a variety of systems, theoretical models, extraction algorithms and calibration methods. In addition to conventional solid dielectric materials, the measurement of artificial metamaterials, liquid, and gaseous-phased samples are separately investigated. The pros of free-space material extraction methods are then compared with resonance and transmission line methods, and their future perspective is presented in the concluding part.
    • Volatile Liquid Detection by Terahertz Technologies

      Baxter, Harry W.; Worrall, Adam A.; Pang, Jie; Chen, Riqing; Yang, Bin; University of Chester; Fujian Agriculture and Forestry University (Frontiers Media, 2021-04-08)
      The prospect of being able to move through security without the inconvenience of separating liquids from bags is an exciting one for passengers, and there are important operational benefits for airports as well. Here, two terahertz (THz) systems, 100 GHz sub-THz line scanner and attenuation total reflection-based THz time domain spectroscopy (TDS), have been used to demonstrate the capability of identifying different liquid samples. Liquid samples’ THz complex permittivities are measured and their differences have contributed to the variation of 100 GHz 2D images of volatile liquids with different volumes inside of cannister bottles. The acquired attenuation images at 100 GHz can easily be used to distinguish highly absorbed liquids (Water, Ethanol, Fuel Treatment Chemicals) and low loss liquids (Petrol, Diesel, Kerosene and Universal Bottle Cleaner). The results give a promising feasibility for mm-wave imager and THz spectroscopy to efficiently identify different volatile liquids.
    • New Extremal Binary Self-dual Codes from block circulant matrices and block quadratic residue circulant matrices

      Gildea, Joe; Kaya, Abidin; Taylor, Rhian; Tylyshchak, Alexander; Yildiz, Bahattin; University of Chester; Sampoerna University; Uzhgorod National University; Northern Arizona University (Elsevier, 2021-08-20)
      In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2 + uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.
    • Virtual reality training in cardiopulmonary resuscitation in schools

      Rees, Nigel; John, Nigel W.; Beever, Lee; Vaughan, Neil; Powell, C; Fletcher, A; Welsh Ambulance Services NHS Trust; Swansea University; University of Chester; University of Exeter; British Heart Foundation; London School of Hygiene & Tropical Medicine (Mark Allen Healthcare, 2021-09-11)
      UK average survival from Out of Hospital Cardiac Arrest (OHCA) survival is around 8.6%, which is significantly lower than other high performing countries with survival rates of over 20%. A cardiac arrest victim is 2–4 times more likely to survive OHCA with bystander CPR provision. Mandatory Teaching CPR to children in school is acknowledged to be the most effective way to reach the entire population and improving the bystander CPR rate and is endorsed by the World Health Organization (WHO) “Kids Save Lives” statement. Despite this, Wales is yet to follow other home nations by including CPR training as a mandatory within the school’s curriculum. In this paper, we explore the role of teaching CPR to schoolchildren and report on the development by Computer scientists at the University of Chester and the Welsh Ambulance Services NHS Trust (WAST) of VCPR, a virtual environment to help teach the procedure. VCPR was developed in three stages: identifying requirements and specifications; development of a prototype; and management—development of software, further funding and exploring opportunities for commercialisation. We describe the opportunities in Wales to skill up the whole population over time in CPR and present our Virtual reality (VR) technology is emerging as a powerful for teaching CPR in schools.
    • Optomechanical switching of adsorption configurations of polar organic molecules by UV radiation pressure

      Arumugam, Kowsalya; Papadopoulos, Theodoros; Tang, Shu-Jung; National Tsing Hua University; Tokyo University of Science; National Synchrotron Radiation Research Center (NSRRC); University of Chester
      Using photoemission spectroscopy (PES), we have systematically investigated the behavior of polar organic molecule, chloroaluminum phthalocyanine (ClAlPc), adsorbed in the Cl-down configuration on the Ag(111) substrate at low temperature − 195 °C under UV irradiation with a range of different photon fluxes. Judging from the evolution of photoemission spectral line shapes of molecular energy states, we discovered that the Cl atoms are so robustly anchored at Ag(111) that the impinging photons cannot flip the ClAlPc molecules, but instead they crouch them down due to radiation pressure; we observe that the phthalocyanine (Pc) lobes bend down to interact with Ag atoms on the substrate and induce charge transfer from them. As photon flux is increased, radiation pressure on the Pc plane initiates tunneling of the Cl atom through the molecular plane to turn the adsorption configuration of ClAlPc from Cl-down to an upheld Cl-up configuration, elucidating an optomechanical way of manipulating the dipole direction of polar molecules. Finally, work function measurements provide a distinct signature of the resulting upheld Cl-up configuration as it leads to a large increase in vacuum level (VL), ~ 0.4 eV higher than that of a typical flat-on Cl-up configuration driven by thermal annealing.
    • New Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighbours

      Gildea, Joe; Kaya, Abidin; Roberts, Adam; Taylor, Rhian; Tylyshchak, Alexander; University of Chester; Harmony Public Schools; Uzhgorod National University (American Institute of Mathematical Sciences, 2021-09-01)
      In this paper, we construct new self-dual codes from a construction that involves a unique combination; $2 \times 2$ block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings $\FF_2$, $\FF_2+u\FF_2$ and $\FF_4+u\FF_4$. Using extensions and neighbours of codes, we construct $32$ new self-dual codes of length $68$. We construct 48 new best known singly-even self-dual codes of length 96.
    • Non-Exhaust Vehicle Emissions of Particulate Matter and VOC from Road Traffic: A Review

      Harrison, Roy; Allan, James; Caruthers, David; Heal, Matthew; Lewis, Alastair; Marner, Ben; Murrells, Tim; Williams, Andrew; University of Birmingham; University of Manchester; Cambridge Environmental Research Consultants; University of Edinburgh; University of York; Air Quality Consultants; Ricardo Energy and Environment; University of Chester; King Abdulaziz University (Elsevier, 2021-07-01)
      As exhaust emissions of particles and volatile organic compounds (VOC) from road vehicles have progressively come under greater control, non-exhaust emissions have become an increasing proportion of the total emissions, and in many countries now exceed exhaust emissions. Non-exhaust particle emissions arise from abrasion of the brakes and tyres and wear of the road surface, as well as from resuspension of road dusts. The national emissions, particle size distributions and chemical composition of each of these sources is reviewed. Most estimates of airborne concentrations derive from the use of chemical tracers of specific emissions; the tracers and airborne concentrations estimated from their use are considered. Particle size distributions have been measured both in the laboratory and in field studies, and generally show particles to be in both the coarse (PM2.5-10) and fine (PM2.5) fractions, with a larger proportion in the former. The introduction of battery electric vehicles is concluded to have only a small effect on overall road traffic particle emissions. Approaches to numerical modelling of non-exhaust particles in the atmosphere are reviewed. Abatement measures include engineering controls, especially for brake wear, improved materials (e.g. for tyre wear) and road surface cleaning and dust suppressants for resuspension. Emissions from solvents in screen wash and de-icers now dominate VOC emissions from traffic in the UK, and exhibit a very different composition to exhaust VOC emissions. Likely future trends in non-exhaust particle emissions are described.
    • Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise

      Yan, Yubin; Kang, Wenyan; Egwu, Bernard; Pani, Amiya; University of Chester, Lvliang University, P. R. China, Indian Institute of Technology Bombay
      A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence, uniqueness and regularity results, we approximate the noise with the piecewise constant function in time in order to obtain a regularized stochastic fractional subdiffusion problem. The regularized problem is then approximated by using the finite element method in spatial direction. The mean squared errors are proved based on the sharp estimates of the various Mittag-Leffler functions involved in the integrals. Numerical experiments are conducted to show that the numerical results are consistent with the theoretical findings.
    • The Potential of Incremental Forming Techniques for Aerospace Applications

      de Sousa, Ricardo Alves; Afonso, Daniel; Rubino, Filice; Behera, Amar Kumar; University of Aveiro; King Juan Carlos University; University of Chester
      Incremental sheet metal forming (ISF) processes are part of a set of non-classical techniques that allow producing low-batches, customized and/or specific geometries for advanced engineering applications, such as aerospace, automotive and biomedical parts. Combined or not with other joining processes and additive manufacturing techniques, ISF processes permit rapid prototyping frameworks, and can be included in the class of smart manufacturing processes. This chapter discusses the fundamentals of ISF technology, key attributes, future challenges and presents few examples related to the use of incremental forming for the development of complex parts as specifically found in aerospace applications such as aerofoils. The use of incremental forming to produce customized designs and to perform quick try-outs of ready-to-use parts contributes to decrease the time to market, decrease tooling cost and increase part design freedom.
    • New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction.

      Gildea, Joe; Korban, Adrian; Roberts, Adam; University of Chester (Elsevier, 2021-05-31)
      In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta \in \{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.
    • Design and finite element simulation of metal-core piezoelectric fiber/epoxy matrix composites for virus detection

      Wang, Yinli; Shi, Yu; Narita, Fumio; Tohoku University; University of Chester
      Undoubtedly, the coronavirus disease 2019 (COVID-19) has received the greatest concern with a global impact, and this situation will continue for a long period of time. Looking back in history, airborne transimission diseases have caused huge casualties several times. COVID-19 as a typical airborne disease caught our attention and reminded us of the importance of preventing such diseases. Therefore, this study focuses on finding a new way to guard against the spread of these diseases such as COVID-19. This paper studies the dynamic electromechanical response of metal-core piezoelectric fiber/epoxy matrix composites, designed as mass load sensors for virus detection, by numerical modelling. The dynamic electromechanical response is simulated by applying an alternating current (AC) electric field to make the composite vibrate. Furthermore, both concentrated and distributed loads are considered to assess the sensitivity of the biosensor during modelling of the combination of both biomarker and viruses. The design parameters of this sensor, such as the resonant frequency, the position and size of the biomarker, will be studied and optimized as the key values to determine the sensitivity of detection. The novelty of this work is to propose functional composites that can detect the viruses from changes of the output voltage instead of the resonant frequency change using piezoelectric sensor and piezoelectric actuator. The contribution of this detection method will significantly shorten the detection time as it avoids fast Fourier transform (FFT) or discrete Fourier transform (DFT). The outcome of this research offers a reliable numerical model to optimize the design of the proposed biosensor for virus detection, which will contribute to the production of high-performance piezoelectric biosensors in the future.
    • 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.