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Group rings: Units and their applications in selfdual codesThe initial research presented in this thesis is the structure of the unit group of the group ring Cn x D6 over a field of characteristic 3 in terms of cyclic groups, specifically U(F3t(Cn x D6)). There are numerous applications of group rings, such as topology, geometry and algebraic Ktheory, but more recently in coding theory. Following the initial work on establishing the unit group of a group ring, we take a closer look at the use of group rings in algebraic coding theory in order to construct selfdual and extremal selfdual codes. Using a well established isomorphism between a group ring and a ring of matrices, we construct certain selfdual and formally selfdual codes over a finite commutative Frobenius ring. There is an interesting relationships between the Automorphism group of the code produced and the underlying group in the group ring. Building on the theory, we describe all possible group algebras that can be used to construct the wellknown binary extended Golay code. The double circulant construction is a wellknown technique for constructing selfdual codes; combining this with the established isomorphism previously mentioned, we demonstrate a new technique for constructing selfdual codes. New theory states that under certain conditions, these selfdual codes correspond to unitary units in group rings. Currently, using methods discussed, we construct 10 new extremal selfdual codes of length 68. In the search for new extremal selfdual codes, we establish a new technique which considers a double bordered construction. There are certain conditions where this new technique will produce selfdual codes, which are given in the theoretical results. Applying this new construction, we construct numerous new codes to verify the theoretical results; 1 new extremal selfdual code of length 64, 18 new codes of length 68 and 12 new extremal selfdual codes of length 80. Using the well established isomorphism and the common four block construction, we consider a new technique in order to construct selfdual codes of length 68. There are certain conditions, stated in the theoretical results, which allow this construction to yield selfdual codes, and some interesting links between the group ring elements and the construction. From this technique, we construct 32 new extremal selfdual codes of length 68. Lastly, we consider a unique construction as a combination of block circulant matrices and quadratic circulant matrices. Here, we provide theory surrounding this construction and conditions for full effectiveness of the method. Finally, we present the 52 new selfdual codes that result from this method; 1 new selfdual code of length 66 and 51 new selfdual codes of length 68. Note that different weight enumerators are dependant on different values of β. In addition, for codes of length 68, the weight enumerator is also defined in terms of γ, and for codes of length 80, the weight enumerator is also de ned in terms of α.

An experimental and computational investigation of pressurised anaerobic digestionThe aim of this work is to gain a greater understanding of the effect of headspace pressure on biogas production from anaerobic digestion. This is important to improve the energy content of the biogas i.e., increase the methane content and therefore reduce the need for upgrading to scrub out carbon dioxide. In addition, headspace pressure can potentially be used to provide energy for mixing and gas sparging, thereby removing the need for mechanical agitation. In this work, an existing computational model was adapted to investigate its prediction of the variation of biogas production as headspace pressure is increased above atmospheric. The simulation results were accompanied with experimental work using periodic venting of sealed laboratory bottles. The headspace pressure was inferred from the weight loss during venting to atmosphere. In addition, a fully instrumented, pressurised digestor system was designed and constructed in which headspace pressure could be measured directly. Experiments were conducted with headspace pressures of up to 3.4 barg. The biogas that accumulated in the headspace during the digestion process was sampled periodically to determine its composition. The results showed that biogas produced at higher pressures has a higher methane content. A mass balance for the headspace sampling process, which assumed no gas was released from the liquid during sampling, was compared to experimental measurements. This led to the discovery that the effective Henry’s constant for the solubility of carbon dioxide could be an order of magnitude lower in digestate than the known value for pure water. Both the adapted model and the laboratoryscale experiments showed that as the headspace pressure increases, the production rate of biogas decreases. The adapted model also gives slightly higher methane content for higher pressure. The model was then used to estimate the specific growth rates of bacteria used in the laboratoryscale experiments and the agreement was not good, which indicates further changes to the model are needed. The results show that the rate of biogas production reduces as the headspace pressure increases but the rate of decrease is not very steep. This same trend was also displayed for yeast fermentation, which was also studied as another model process for pressurised biological gas production. The variation of the rate of 𝐶𝑂2 evolution with pressure was also used to infer the concentration of dissolved 𝐶𝑂2 within the fermenting yeast cells. Finally, turning attention back to anaerobic digestion processes for energy, it is encouraging that at the relatively modest elevation of pressure required for sparging to give mixing (less than 0.5 barg), the reduction in biogas evolution is small. This small penalty might therefore be offset in a production scale system by the reduced costs of mixing and increased methane content of the biogas.

Modified magnetic coreshell mesoporous silica nanoformulations with encapsulated quercetin exhibit antiamyloid and antioxidant activityTargeted tissue drug delivery is a challenge in contemporary nanotechnologically driven therapeutic approaches, with the interplay interactions between nanohost and encapsulated drug shaping the ultimate properties of transport, release and efficacy of the drug at its destination. Prompted by the need to pursue the synthesis of such hybrid systems, a family of modified magnetic coreshell mesoporous silica nanoformulations was synthesized with encapsulated quercetin, a natural flavonoid with proven bioactivity. The new nanocarriers were produced via the solgel process, using tetraethoxysilane as a precursor and bearing a magnetic core of surfacemodified monodispersed magnetite colloidal superparamagnetic nanoparticles, subsequently surfacemodified with polyethylene glycol 3000 (PEG3k). The arising nanoformulations were evaluated for their textural and structural properties, exhibiting enhanced solubility and stability in physiological media, as evidenced by the loading capacity, entrapment efficiency results and in vitro release studies of their load. Guided by the increased bioavailability of quercetin in its encapsulated form, further evaluation of the biological activity of the magnetic as well as nonmagnetic coreshell nanoparticles, pertaining to their antiamyloid and antioxidant potential, revealed interference with the aggregation of βamyloid peptide (Aβ) in Alzheimer’s disease, reduction of Aβ cellular toxicity and minimization of Aβinduced Reactive Oxygen Species (ROS) generation. The data indicate that the biological properties of released quercetin are maintained in the presence of the host nanocarriers. Collectively, the findings suggest that the emerging hybrid nanoformulations can function as efficient nanocarriers of hydrophobic natural flavonoids in the development of multifunctional nanomaterials toward therapeutic applications.

A Framework for WebBased Immersive AnalyticsThe emergence of affordable Virtual Reality (VR) interfaces has reignited the interest of researchers and developers in exploring new, immersive ways to visualise data. In particular, the use of openstandards Webbased technologies for implementing VR experiences in a browser aims to enable their ubiquitous and platformindependent adoption. In addition, such technologies work in synergy with established visualization libraries, through the HTML Document Object Model (DOM). However, creating Immersive Analytics (IA) experiences remains a challenging process, as the systems that are currently available require knowledge of game engines, such as Unity, and are often intrinsically restricted by their development ecosystem. This thesis presents a novel approach to the design, creation and deployment of Immersive Analytics experiences through the use of openstandards Web technologies. It presents <VRIA>, a Webbased framework for creating Immersive Analytics experiences in VR that was developed during this PhD project. <VRIA> is built upon WebXR, AFrame, React and D3.js, and offers a visualization creation workflow which enables users of different levels of expertise to rapidly develop Immersive Analytics experiences for the Web. The aforementioned reliance on open standards and the synergies with popular visualization libraries make <VRIA> ubiquitous and platformindependent in nature. Moreover, by using WebXR’s progressive enhancement, the experiences <VRIA> is able to create are accessible on a plethora of devices. This thesis presents an elaboration on the motivation for focusing on openstandards Web technologies, presents the <VRIA> visualization creation workflow and details the underlying mechanics of our framework. It reports on optimisation techniques, integrated into <VRIA>, that are necessary for implementing Immersive Analytics experiences with the necessary performance profile on the Web. It discusses scalability implications of the framework and presents a series of use case applications that demonstrate the various features of <VRIA>. Finally, it describes the lessons learned from the development of the framework, discusses current limitations, and outlines further extensions.

SelfDual Codes using Bisymmetric Matrices and Group RingsIn this work, we describe a construction in which we combine together the idea of a bisymmetric matrix and group rings. Applying this construction over the ring F4 + uF4 together with the well known extension and neighbour methods, we construct new selfdual codes of length 68: In particular, we find 41 new codes of length 68 that were not known in the literature before.

2^n Bordered Constructions of SelfDual codes from Group RingsSelfdual codes, which are codes that are equal to their orthogonal, are a widely studied family of codes. Various techniques involving circulant matrices and matrices from group rings have been used to construct such codes. Moreover, families of rings have been used, together with a Gray map, to construct binary selfdual codes. In this paper, we introduce a new bordered construction over group rings for selfdual codes by combining many of the previously used techniques. The purpose of this is to construct selfdual codes that were missed using classical construction techniques by constructing selfdual codes with diﬀerent automorphism groups. We apply the technique to codes over ﬁnite commutative Frobenius rings of characteristic 2 and several group rings and use these to construct interesting binary selfdual codes. In particular, we construct some extremal selfdual codes length 64 and 68, constructing 30 new extremal selfdual codes of length 68.

Optimization of antiwear and antibacterial properties of beta TiNb alloy via controlling duty cycle in openair laser nitridingA multifunctional beta TiNb surface, featuring wearresistant and antibacterial properties, was successfully created by means of openair 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, openair 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, antifriction, antiwear and antibacterial 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

An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated spacetime white noiseWe consider the strong convergence of the numerical methods for solving stochastic subdiffusion problem driven by an integrated spacetime white noise. The time fractional derivative is approximated by using the L1 scheme and the time fractional integral is approximated with the Lubich's first order convolution quadrature formula. We use the Euler method to approximate the noise in time and use the truncated series to approximate the noise in space. The spatial variable is discretized by using the linear finite element method. Applying the idea in Gunzburger \et (Math. Comp. 88(2019), pp. 17151741), we express the approximate solutions of the fully discrete scheme by the convolution of the piecewise constant function and the inverse Laplace transform of the resolvent related function. Based on such convolution expressions of the approximate solutions, we obtain the optimal convergence orders of the fully discrete scheme in spatial multidimensional cases by using the Laplace transform method and the corresponding resolvent estimates.

New binary selfdual codes via a generalization of the four circulant constructionIn this work, we generalize the four circulant construction for selfdual codes. By applying the constructions over the alphabets $\mathbb{F}_2$, $\mathbb{F}_2+u\mathbb{F}_2$, $\mathbb{F}_4+u\mathbb{F}_4$, we were able to obtain extremal binary selfdual codes of lengths 40, 64 including new extremal binary selfdual codes of length 68. More precisely, 43 new extremal binary selfdual codes of length 68, with rare new parameters have been constructed.

Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth DataTwo higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwaldLetnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 27032727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $ O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results.

A Modified Bordered Construction for SelfDual Codes from Group RingsWe describe a bordered construction for selfdual codes coming from group rings. We apply the constructions coming from the cyclic and dihedral groups over several alphabets to obtain extremal binary selfdual codes of various lengths. In particular we find a new extremal binary selfdual code of length 78.

Interactive ThreeDimensional Simulation and Visualisation of Real Time Blood Flow in Vascular NetworksOne of the challenges in cardiovascular disease management is the clinical decisionmaking process. When a clinician is dealing with complex and uncertain situations, the decision on whether or how to intervene is made based upon distinct information from diverse sources. There are several variables that can affect how the vascular system responds to treatment. These include: the extent of the damage and scarring, the efficiency of blood flow remodelling, and any associated pathology. Moreover, the effect of an intervention may lead to further unforeseen complications (e.g. another stenosis may be “hidden” further along the vessel). Currently, there is no tool for predicting or exploring such scenarios. This thesis explores the development of a highly adaptive realtime simulation of blood flow that considers patient specific data and clinician interaction. The simulation should model blood realistically, accurately, and through complex vascular networks in realtime. Developing robust flow scenarios that can be incorporated into the decision and planning medical tool set. The focus will be on specific regions of the anatomy, where accuracy is of the utmost importance and the flow can develop into specific patterns, with the aim of better understanding their condition and predicting factors of their future evolution. Results from the validation of the simulation showed promising comparisons with the literature and demonstrated a viability for clinical use.

The past, present and future of indoor air chemistryThis is an editorial contribution to the Journal Indoor Air on the future direction of indoor air chemistry research.

Finitetime blowup of a nonlocal stochastic parabolic problemThe main aim of the current work is the study of the conditions under which (finitetime) blowup of a nonlocal stochastic parabolic problem occurs. We first establish the existence and uniqueness of the localintime weak solution for such problem. The first part of the manuscript deals with the investigation of the conditions which guarantee the occurrence of noiseinduced blowup. In the second part we first prove the $C^{1}$spatial regularity of the solution. Then, based on this regularity result, and using a strong positivity result we derive, for first in the literature of SPDEs, a Hopf's type boundary value point lemma. The preceding results together with Kaplan's eigenfunction method are then employed to provide a (nonlocal) drift term induced blowup result. In the last part of the paper, we present a method which provides an upper bound of the probability of (nonlocal) drift term induced blowup.

Graphene Oxide Bulk Modified ScreenPrinted Electrodes Provide Beneficial Electroanalytical Sensing CapabilitiesWe demonstrate a facile methodology for the mass production of graphene oxide (GO) bulk modified screenprinted electrodes (GOSPEs) that are economical, highly reproducible and provide analytically useful outputs. Through fabricating GOSPEs with varying percentage mass incorporations (2.5, 5, 7.5 and 10%) of GO, an electrocatalytic effect towards the chosen electroanalytical probes is observed, that increases with greater GO incorporated compared to bare/ graphite SPEs. The optimum mass ratio of 10% GO to 90% carbon ink displays an electroanalytical signal towards dopamine (DA) and uric acid (UA), which is ca. ×10 greater in magnitude than that achievable at a bare/unmodified graphite SPE. Furthermore, 10% GOSPEs exhibit a competitively low limit of detection (3σ) towards DA at ca. 81 nM, which is superior to that of a bare/unmodified graphite SPE at ca. 780 nM. The improved analytical response is attributed to the large number of oxygenated species inhabiting the edge and defect sites of the GO nanosheets, which are available to exhibit electrocatalytic responses towards innersphere electrochemical analytes. Our reported methodology is simple, scalable, and cost effective for the fabrication of GOSPEs, that display highly competitive LODs, and is of significant interest for use in commercial and medicinal applications

Mathematical Modelling of DNA MethylationDNA methylation is a key epigenetic process which has been intimately associated with gene regulation. In recent years growing evidence has associated DNA methylation status with a variety of diseases including cancer, Alzheimer’s disease and cardiovascular disease. Moreover, changes to DNA methylation have also recently been implicated in the ageing process. The factors which underpin DNA methylation are complex, and remain to be fully elucidated. Over the years mathematical modelling has helped to shed light on the dynamics of this important molecular system. Although the existing models have contributed significantly to our overall understanding of DNA methylation, they fall short of fully capturing the dynamics of this process. In this work DNA methylation models are developed and improved and their suitability is demonstrated through mathematical analysis and computational simulation. In particular, a linear and nonlinear deterministic model are developed which capture more fully the dynamics of the key intracellular events which characterise DNA methylation. Furthermore, uncertainty is introduced into the model to describe the presence of intrinsic and extrinsic cell noise. This way a stochastic model is constructed and presented which accounts for the stochastic nature in cell dynamics. One of the key predictions of the model is that DNA methylation dynamics do not alter when the quantity of DNA methylation enzymes change. In addition, the nonlinear model predicts DNA methylation promoter bistability, which is commonly observed experimentally. Moreover, a new way of modelling DNA methylation uncertainty is introduced.

Numerical methods for deterministic and stochastic fractional partial differential equationsIn this thesis we will explore the numerical methods for solving deterministic and stochastic space and time fractional partial differential equations. Firstly we consider Fourier spectral methods for solving some linear stochastic space fractional partial differential equations perturbed by spacetime white noises in one dimensional case. The space fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject to some boundary conditions. We approximate the spacetime white noise by using piecewise constant functions and obtain the approximated stochastic space fractional partial differential equations. The approximated stochastic space fractional partial differential equations are then solved by using Fourier spectral methods. Secondly we consider Fourier spectral methods for solving stochastic space fractional partial differential equation driven by special additive noises in one dimensional case. The space fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject to some boundary conditions. The spacetime noise is approximated by the piecewise constant functions in the time direction and by appropriate approximations in the space direction. The approximated stochastic space fractional partial differential equation is then solved by using Fourier spectral methods. Thirdly, we will consider the discontinuous Galerkin time stepping methods for solving the linear space fractional partial differential equations. The space fractional derivatives are defined by using Riesz fractional derivative. The space variable is discretized by means of a Galerkin finite element method and the time variable is discretized by the discontinous Galerkin method. The approximate solution will be sought as a piecewise polynomial function in t of degree at most q−1, q ≥ 1, which is not necessarily continuous at the nodes of the defining partition. The error estimates in the fully discrete case are obtained and the numerical examples are given. Finally, we consider error estimates for the modified L1 scheme for solving time fractional partial differential equation. Jin et al. (2016, An analysis of the L1 scheme for the subdiffifusion equation with nonsmooth data, IMA J. of Number. Anal., 36, 197221) ii established the O(k) convergence rate for the L1 scheme for both smooth and nonsmooth initial data. We introduce a modified L1 scheme and prove that the convergence rate is O(k2−α=), 0 < α < 1 for both smooth and nonsmooth initial data. We first write the time fractional partial differential equations as a Volterra integral equation which is then approximated by using the convolution quadrature with some special generating functions. A Laplace transform method is used to prove the error estimates for the homogeneous time fractional partial differential equation for both smooth and nonsmooth data. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Gcodes over Formal Power Series Rings and Finite Chain RingsIn this work, we define $G$codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$. We show that the dual of a $G$code is again a $G$code in this setting. We study the projections and lifts of $G$codes over the finite chain rings and over the formal power series rings respectively. We extend known results of constructing $\gamma$adic codes over $R_\infty$ to $\gamma$adic $G$codes over the same ring. We also study $G$codes over principal ideal rings.

New Extremal SelfDual Binary Codes of Length 68 via Composite Construction, F2 + uF2 Lifts, Extensions and NeighborsWe describe a composite construction from group rings where the groups have orders 16 and 8. This construction is then applied to find the extremal binary selfdual codes with parameters [32, 16, 8] or [32, 16, 6]. We also extend this composite construction by expanding the search field which enables us to find more extremal binary selfdual codes with the above parameters and with different orders of automorphism groups. These codes are then lifted to F2 + uF2, to obtain extremal binary images of codes of length 64. Finally, we use the extension method and neighbor construction to obtain new extremal binary selfdual codes of length 68. As a result, we obtain 28 new codes of length 68 which were not known in the literature before.

Terahertz Probing Irreversible Phase Transitions Related to Polar Clusters in Bi0.5Na0.5TiO3based FerroelectricElectricfieldinduced phase transitions in Bi0.5Na0.5TiO3 (BNT)based relaxor ferroelectrics are essential to the controlling of their electrical properties and consequently in revolutionizing their dielectric and piezoelectric applications. However, the fundamental understanding of these transitions is a longstanding challenge due to their complex crystal structures. Given the structural inhomogeneity at the nanoscale or subnanoscale in these materials, dielectric response characterization based on terahertz (THz) electromagneticprobe beamfields, is intrinsically coordinated to lattice dynamics during DCbiased poling cycles. The complex permittivity reveals the fieldinduced phase transitions to be irreversible. This profoundly counters the claim of reversibility, the conventional support for which, is based upon the peak that is manifest in each of four quadrants of the currentfield curves. The mechanism of this irreversibility is solely attributed to polar clusters in the transformed lattices. These represent an extrinsic factor which is quiescent in the THz spectral domain.