Faculty of Science and Engineering: Recent submissions
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Split spin factor algebrasMotivated by Yabe's classification of symmetric $2$generated axial algebras of Monster type \cite{yabe}, we introduce a large class of algebras of Monster type $(\alpha, \frac{1}{2})$, generalising Yabe's $\mathrm{III}(\alpha,\frac{1}{2}, \delta)$ family. Our algebras bear a striking similarity with Jordan spin factor algebras with the difference being that we asymmetrically split the identity as a sum of two idempotents. We investigate the properties of these algebras, including the existence of a Frobenius form and ideals. In the $2$generated case, where our algebra is isomorphic to one of Yabe's examples, we use our new viewpoint to identify the axet, that is, the closure of the two generating axes.

Enumerating 3generated axial algebras of Monster typeAn axial algebra is a commutative nonassociative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion law as the Griess algebra. The 2generated axial algebras of Monster type, called NortonSakuma algebras, have been fully classified and are one of nine isomorphism types. In this paper, we enumerate a subclass of 3generated axial algebras of Monster type in terms of their groups and shapes. It turns out that the vast majority of the possible shapes for such algebras collapse; that is they do not lead to nontrivial examples. This is in sharp contrast to previous thinking. Accordingly, we develop a method of minimal forbidden configurations, to allow us to efficiently recognise and eliminate collapsing shapes.

A new perspective on the numerical and analytical treatment of a certain singular Volterra integral equationIn this thesis, the focus of our attention is on a certain linear Volterra integral equation with singular kernel. The equation is of great interest due to the fact that, under certain conditions, it possesses an in finite family of solutions, out of which only one has C1continuity. Numerous previous studies have been conducted and a variety of solution methods proposed. However, the emphasis has invariably been on determining just the differentiable solution. Thus, a significant gap in the research relating to this equation was identified and, therefore, our main objective here was to develop an effective solution method that allows us to approximate any chosen solution out of the infinite solution set. To this end, we converted the original integral equation into a singular differential form. Then, by applying a combination of analytical results from functional and real analysis, measure theory and the theory of Lebesgue integration, we reduced the problem to that of solving a regular initial value problem. Numerical methods were then applied and our experimental results proved that our method was highly effective, producing very accurate approximations to the true solution in a comparative study. Therefore, we feel our work here makes a significant contribution in this field of study, both from a theoretical viewpoint, as during the course of our research we established a direct relationship between the nonsmooth solutions of the integral equation and the weak solutions of our differential scheme, and in practice. Integral equations of this form arise in the study of heat conduction, diffusion and in thermodynamics. Therefore, another of our aims was to construct a method that could readily be applied in 'real world' modelling. Thus, as traditional models most often present as differential equations and, furthermore, as our method significantly simplifies the process of computing the solutions, we believe we have achieved this objective. Hence, in the final chapter, we highlight some of the ways in which our method could be adopted in order to help solve some of today's most challenging problems.

An Immersive Hapticenabled Training Simulation for ParamedicsThis paper describes the integration of haptics support into a virtual reality training simulation aimed at skills retention for paramedics. We focus on a chest decompression, a lifesaving invasive procedure used for traumaassociated cardiopulmonary resuscitation (and other causes) that every emergency physician needs to master. It is not regularly performed by a paramedic, however, and therefore skills maintenance is a challenge. In our simulation, a virtual Russell PneumoFix8 device is used to carry out the procedure and it is controlled with the 3D Systems Touch grounded force feedback device. We describe how this device has been integrated into an immersive virtual environment so that it or any other tool can be used at any location in the scene. Quantitative data has been obtained from an evaluation exercise carried out with 21 paramedics. The majority of these participants reported a good feeling of presence, according to the Spatial Presence Experience Scale. They indicated strongly that the use of hapticenabled simulators that include the kind of interaction techniques implemented in our simulator would be beneficial for training and skills retention. The realism of using the simulator at a 1 to 1 scale was also highly scored. A System Usability Scale was also calculated and the results show that the simulator is close to an acceptable standard for usability but more work is needed. We will address this in future work.

Low permittivity cordieritebased microwave dielectric ceramics for 5G/6G telecommunications5G and forthcoming 6G communication systems require dielectric ceramics with low relative permittivity (εr) and nearzero temperature coefficient of resonant frequency (τf) for the lower part of the microwave (MW) band and at subTerahertz. Mg2Al4Si5O18 (MAS) ceramics are promising candidates due to their low εr (~6) and highquality factor (Q×f >40,000 GHz) but have a large f. In this study, 5.5wt% TiO2 (MAST5.5) was used to adjust τf of MAS to 2.8 ppm/℃ whilst retaining low εr (5.24) and good Q×f (33,400 GHz), properties consistent with those obtained by infrared reflectance. A demonstrator microstrip patch antenna with gain 4.92dBi and 76.3% efficiency was fabricated from MAST5.5.

Resolving nanoscopic structuring and interfacial THz dynamics in setting cementsThe setting dynamics of two commercial cements have been tracked over >24 hours of setting with nondestructive THz spectroscopy and neutron scattering. Two established glass ionomer cements (GICs) were measured, both exhibiting similar and commercially agreeable nonlinear settings associated with changes in interfacial particle dynamics through variations in their collective lowenergy vibrations. Structural evolutions in the ∼1–30 nm range were correlated with changes in small angle neutron scattering (SANS) profiles over setting. Accompanying models of the interfacial structures and the amorphous glass components of the cements helped make the dynamic and structural trends comprehensible. The combined observations helped elucidate key temporal features in the setting of the cements, whilst suggesting the functional role played by the THz vibrations, in particular at dynamically coordinated interfacial Alatom pivots. The insights obtained could help evolve nanoscopic strategies to optimise cements and their eventual properties.

CAP: Patching the Human VulnerabilityCyber threats to organisations across all industries are increasing in both volume and complexity, leading to significant, and sometimes severe, consequences. The common weakest link in organisations security is the human vulnerability. The sudden popularity of remoteworking due to the Covid19 pandemic opened organisations and their employees up to more risks, particularly as many workers believe that they are more distracted when at home. Existing cyber training using a ‘onesizefitsall’ approach has been proven inefficient/ineffective and the need for a more fitforpurpose training is required. When it comes to cyber training, we know that there is no singletrainingfitsall solution – people have different technical skills, different prior knowledge and experience, are in different roles, exposed to different security risks, and require knowledge that is relevant to what they do. This study makes a case for tailored rolebased cybersecurity training suitable for awareness within organisations across multiple industries. The study explores the strengths and weaknesses of existing cyber training and literature to make recommendations on efficient awareness and training programme strategies. The study carries out knowledge and task analysis of job roles to create profiles of skills and knowledge they require. These are grouped by topic and level to form scenariobased multiplechoice questions which are mapped to create a Cyber Awareness Platform (CAP). A CAP prototype is introduced as a flexible webbased system allowing users to assess their prior knowledge and skills personalised to their role. Knowledge gaps and training needs are identified, and recommendations are tailored to the individual. Initial analysis of CAP shows promising results, indicating that such rolesensitive solution would be highly beneficial to users. This offers further development opportunities in producing an allinone cyber assessment and training platform.

Forensic Trails Obfuscation and Preservation via Hard Drive FirmwareThe hard disk drive stores data the user is creating, modifying, and deleting while a firmware facilitates communication between the drive and the operating system. The firmware tells the device and machine how to communicate with each other and will share useful information such as, disk size and information on any bad sectors. Current research shows that exploits exist that can manipulate these outputs. As an attacker, you can change the size of the disk displayed to the operating system to hide data in, likewise by marking an area of the disk as bad. Users may not be aware of these changes as the operating system will accept the readings from the firmware. However, although the data is not reachable via the operating system this paper looks at the traceability of manipulated data using data recovery software FTK Imager, Recuva, EaseUS and FEX Imager. This report examines the use of malicious techniques to thwart digital forensic procedures by manipulating the firmware. It is shown how this is possible and current forensic techniques or software does not easily detect a change within the firmware. However, with the use of various forensic tools, obfuscated trails are detectable. This report follows a black box testing methodology to show the validation of forensic tools or software against antiforensic techniques. The analysis of the results showed that most tools can find the firmware changes, however, it requires an analyst to spot the subtle differences between standard and manipulated devices. The use of multiple software tools can help an analyst spot the inconsistencies.

Group LCD and group reversible LCD codesIn this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the n × n matrices to obtain LCD codes. Our construction method guarantees that our LCD codes are also group codes, namely, the codes are ideals in a group ring. We show that with a certain condition on the group ring element v, one can construct nontrivial group LCD codes. Moreover, we also show that by adding more constraints on the group ring element v, one can construct group LCD codes that are reversible. We present many examples of binary group LCD codes of which some are optimal and group reversible LCD codes with different parameters.

Electrical resistance tomographybased multimodality sensor and drift flux model for measurement of oil–gas–water flowAbstract: This paper proposes a novel method to measure each constituent of an oil–gas–water mixture in a water continuous flow, typically encountered in many processes. It deploys a dualplane electrical resistance tomography sensor for measuring dispersed phase volume fraction and velocity; a gradiomanometer flow density meter and a drift flux model to estimate slip velocities; with absolute pressure and temperature measurements. These data are fused to estimate constituent volume flow rates. Other commonly used operational parameters can be further derived: water cut or water liquid ratio (WLR) and gas volume fraction (GVF). Trials are described for flow rates of water 5–10 m3 h−1; oil 2–10 m3 h−1 and gas 1–15 m3 h−1. The comparative results are included with published data from the Schlumberger Gould Research flow facility. The paper proposes the use of the described configuration for measurement of volume flow rates in oil–gas–water flows with an absolute error of ±10% within GVF 9%–85% and WLR > 45%.

Binary selfdual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme<p style='textindent:20px;'>We present a generator matrix of the form <inlineformula><texmath id="M1">\begin{document}$ [ \sigma(v_1) \  \ \sigma(v_2)] $\end{document}</texmath></inlineformula>, where <inlineformula><texmath id="M2">\begin{document}$ v_1 \in RG $\end{document}</texmath></inlineformula> and <inlineformula><texmath id="M3">\begin{document}$ v_2\in RH $\end{document}</texmath></inlineformula>, for finite groups <inlineformula><texmath id="M4">\begin{document}$ G $\end{document}</texmath></inlineformula> and <inlineformula><texmath id="M5">\begin{document}$ H $\end{document}</texmath></inlineformula> of order <inlineformula><texmath id="M6">\begin{document}$ n $\end{document}</texmath></inlineformula> for constructing selfdual codes and linear complementary dual codes over the finite Frobenius ring <inlineformula><texmath id="M7">\begin{document}$ R $\end{document}</texmath></inlineformula>. In general, many of the constructions to produce selfdual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find selfdual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve <inlineformula><texmath id="M8">\begin{document}$ 10 $\end{document}</texmath></inlineformula> of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain <inlineformula><texmath id="M9">\begin{document}$ 82 $\end{document}</texmath></inlineformula> new binary linear complementary dual codes, <inlineformula><texmath id="M10">\begin{document}$ 50 $\end{document}</texmath></inlineformula> of which are either optimal or near optimal of lengths <inlineformula><texmath id="M11">\begin{document}$ 41 \leq n \leq 61 $\end{document}</texmath></inlineformula> which are new to the literature.</p>

A numerical exercise on waste incinerationAbstract: A numerical example for tutorial and possibly design exercise use is described which is concerned with the performance of household waste as a fuel in power generation.

Aircraft Electrical Propulsion for HighSpeed Flight: Rim Driven Fan (RDF) TechnologyThe aim of this programme of studies is to research and develop electrical Rim Driven Fan (RDF) technology for highspeed aircraft propulsion and to provide knowledge to support Society’s efforts to combat climate change using zeroemission technologies. The objectives were to conduct research into the stateoftheart of aircraft electrical propulsion, to estimate the performance of single and dual stage contrarotating fans over a range of diameters, to provide a methodology to enable the aerodynamic design and detailed Computational Fluid Dynamic (CFD) analyses of small contrarotating fans and to create a conceptual design for an RDF device suitable to power an unmanned aircraft. In completing this work, literature reviews were carried out on electrically powered propulsion for aircraft, electrical motor technologies and rim drive technology for aircraft propulsion. Original research was undertaken in the form of aerodynamic analyses, using derived numerical and CFD techniques, to determine the optimum performance of single and dual stage (contrarotating) rim driven fans for highspeed electric aircraft applications. Original research was also undertaken in the form of electrical analyses using MotorCAD finite element software to analyse the feasibility of novel rimdrive concepts such as slotless stator designs, aluminium windings and ironless rotors with Halbach magnet arrays in an RDF context. The results of these studies have contributed new knowledge that has been peerreviewed and internationally published. An original RDF design concept, suitable to power an unmanned aircraft, was devised and a UK patent application filed. The main findings of this work are that RDF technology offers a viable means of highspeed aircraft propulsion with a dualstage contrarotating, aircooled fan arrangement. That optimum RDF power density is achieved with slotless windings and ironless rotors configured with Halbach magnet arrays which reduce their rotating mass. These findings have enabled a feasible novel RDF design to be created which is a significant contribution in the field of electrical aircraft propulsion. The results of this work also contribute the significant new knowledge that dual stage contrarotating RDF configurations provide the potential for an increase in thrust per frontal area, and higher exhaustair velocities, when compared with existing hubdriven fan technologies. This work has established a novel fan design technique, that can be used by technologists to analyse and design future electrical fan concepts, and offers a significant contribution towards Society’s efforts to combat climate change with zeroemission technologies. Opportunities for further areas of study in this field are in the analyses of large diameter high thrust versions of RDFs suitable for large manned aircraft and hovercraft applications.

Weak convergence of the L1 scheme for a stochastic subdiffusion problem driven by fractionally integrated additive noiseThe weak convergence of a fully discrete scheme for approximating a stochastic subdiffusion problem driven by fractionally integrated additive noise is studied. The Caputo fractional derivative is approximated by the L1 scheme and the RiemannLiouville fractional integral is approximated with the first order convolution quadrature formula. The noise is discretized by using the Euler method and the spatial derivative is approximated with the linear finite element method. Based on the nonsmooth data error estimates of the corresponding deterministic problem, the weak convergence orders of the fully discrete schemes for approximating the stochastic subdiffusion problem driven by fractionally integrated additive noise are proved by using the Kolmogorov equation approach. Numerical experiments are given to show that the numerical results are consistent with the theoretical results.

Numerical methods for CaputoHadamard fractional differential equations with graded and nonuniform meshesWe consider the predictorcorrector numerical methods for solving CaputoHadamard fractional differential equation with the graded meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \big ( \frac{j}{N} \big )^{r}, \, j=0, 1, 2, \dots, N$ with $a \geq 1$ and $ r \geq 1$, where $\log a = \log t_{0} < \log t_{1} < \dots < \log t_{N}= \log T$ is a partition of $[\log t_{0}, \log T]$. We also consider the rectangular and trapezoidal methods for solving CaputoHadamard fractional differential equation with the nonuniform meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \frac{j (j+1)}{N(N+1)}, \, j=0, 1, 2, \dots, N$. Under the weak smoothness assumptions of the CaputoHadamard fractional derivative, e.g., $\prescript{}{CH}D^\alpha_{a,t}y(t) \notin C^{1}[a, T]$ with $ \alpha \in (0, 2)$, the optimal convergence orders of the proposed numerical methods are obtained by choosing the suitable graded mesh ratio $r \geq 1$. The numerical examples are given to show that the numerical results are consistent with the theoretical findings.

A novel genetic search scheme based on natureinspired evolutionary algorithms for binary selfdual codesIn this paper, a genetic algorithm, one of the evolutionary algorithm optimization methods, is used for the first time for the problem of computing extremal binary selfdual codes. We present a comparison of the computational times between the genetic algorithm and a linear search for different size search spaces and show that the genetic algorithm is capable of computing binary selfdual codes significantly faster than the linear search. Moreover, by employing a known matrix construction together with the genetic algorithm, we are able to obtain new binary selfdual codes of lengths 68 and 72 in a significantly short time. In particular, we obtain 11 new binary selfdual codes of length 68 and 17 new binary selfdual codes of length 72.

New type I binary $[72, 36, 12]$ selfdual codes from $M_6(\mathbb{F}_2)G$  Group matrix rings by a hybrid search technique based on a neighbourhoodvirus optimisation algorithmIn this paper, a new search technique based on a virus optimisation algorithm is proposed for calculating the neighbours of binary selfdual codes. The aim of this new technique is to calculate neighbours of selfdual codes without reducing the search field in the search process (this technique is known in the literature due to the computational time constraint) but still obtaining results in a reasonable time (significantly faster when compared to the standard linear computational search). We employ this new search algorithm to the wellknown neighbour method and its extension, the $ k^{th} $ range neighbours, and search for binary $ [72, 36, 12] $ selfdual codes. In particular, we present six generator matrices of the form $ [I_{36} \  \ \tau_6(v)], $ where $ I_{36} $ is the $ 36 \times 36 $ identity matrix, $ v $ is an element in the group matrix ring $ M_6(\mathbb{F}_2)G $ and $ G $ is a finite group of order 6, to which we employ the proposed algorithm and search for binary $ [72, 36, 12] $ selfdual codes directly over the finite field $\mathbb{F}_2 $. We construct 1471 new Type I binary $ [72, 36, 12] $ selfdual codes with the rare parameters $ \gamma = 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32 $\ in their weight enumerators.

2D‐Hexagonal Boron Nitride Screen‐Printed Bulk‐Modified Electrochemical Platforms Explored towards Oxygen Reduction ReactionsA low‐cost, scalable and reproducible approach for the mass production of screen‐printed electrode (SPE) platforms that have varying percentage mass incorporations of 2D hexagonal boron nitride (2D‐hBN) (2D‐hBN/SPEs) is demonstrated herein. These novel 2D‐hBN/SPEs are explored as a potential metal‐free electrocatalysts towards oxygen reduction reactions (ORRs) within acidic media where their performance is evaluated. A 5% mass incorporation of 2D‐hBN into the SPEs resulted in the most beneficial ORR catalysis, reducing the ORR onset potential by ca. 200 mV in comparison to bare/unmodified SPEs. Furthermore, an increase in the achievable current of 83% is also exhibited upon the utilisation of a 2D‐hBN/SPE in comparison to its unmodified equivalent. The screen‐printed fabrication approach replaces the less‐reproducible and time‐consuming dropcasting technique of 2D‐hBN and provides an alternative approach for the large‐scale manufacture of novel electrode platforms that can be utilised in a variety of applications

Visualization for Epidemiological Modelling: Challenges, Solutions, Reflections & RecommendationsWe report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs – a series of ideas, approaches and methods taken from existing visualization research and practice – deployed and developed to support modelling of the COVID19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type; and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. https://rampvis.github.io/RAMPVISPhilTransASupplement/