Browsing Faculty of Science and Engineering by Title
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Graphite ScreenPrinted Electrodes Applied for the Accurate and Reagentless Sensing of pHA reagentless pH sensor based upon disposable and economical graphite screenprinted electrodes (GSPEs) is demonstrated for the first time. The voltammetric pH sensor utilises GSPEs which are chemically pretreated to form surface immobilised oxygenated species that when their redox behaviour is monitored, give a Nernstian response over a large pH range (113). An excellent experimental correlation is observed between the voltammetric potential and pH over the entire pH range of 113, such a response is not usually expected but rather deviation from linearity is encountered at alkaline pH values; absence of this has previously been attributed to a change in pKa value of surface immobilised groups. This nondeviation, which is observed here in the case of our facile produced reagentless pH sensor and also reported in the literature for pH sensitive compounds immobilized upon carbon electrodes/surfaces,where a linear response is observed over the entire pH range, is explained alternatively for the first time. The performance of the GSPE pH sensor is directly compared with a glass pH probe and applied to the measurement of pH in real samples where an excellent correlation between the two protocols is observed validating the proposed GSPE pH sensor.

Group Codes, Composite Group Codes and Constructions of SelfDual CodesThe main research presented in this thesis is around constructing binary selfdual codes using group rings together with some wellknown 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 selfdual 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 selfdual code over a fi nite commutative Frobenius ring. Together with our generator matrix and some wellknown code construction methods, we find many binary selfdual 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 selfdual 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 Gcodes. We show that these new codes are ideals in the group ring RG and prove that the dual of a composite Gcode is also a composite Gcode. 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 selfdual codes over finite commutative Frobenius rings. Additionally, together with some generator matrices of the type [In  Ω(v)] and the wellknown extension and neighbour methods, we fi nd many new binary selfdual codes with parameters [68, 34, 12]. Lastly in this work, we study composite Gcodes 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∞

Group Rings, GCodes and Constructions of SelfDual and Formally SelfDual CodesWe describe Gcodes, which are codes that 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 Gcode is also a Gcode. We give constructions of selfdual and formally selfdual codes in this setting and we improve the existing construction given in [13] by showing that one of the conditions given in the theorem is unnecessary and, moreover, it restricts the number of selfdual codes obtained by the construction. We show that several of the standard constructions of selfdual codes are found within our general framework. We prove that our constructed codes must have an automorphism group that contains G as a subgroup. We also prove that a common construction technique for producing selfdual codes cannot produce the putative [72, 36, 16] Type II code. Additionally, we show precisely which groups can be used to construct the extremal Type II codes over length 24 and 48. We define quasiG codes and give a construction of these codes.

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.

Halanaytype theory in the context of evolutionary equations with timelagWe consider extensions and modifications of a theory due to Halanay, and the context in which such results may be applied. Our emphasis is on a mathematical framework for Halanaytype analysis of problems with time lag and simulations using discrete versions or numerical formulae. We present selected (linear and nonlinear, discrete and continuous) results of Halanay type that can be used in the study of systems of evolutionary equations with various types of delayed argument, and the relevance and application of our results is illustrated, by reference to delaydifferential equations, difference equations, and methods.

Haptic feedback from human tissues of various stiffness and homogeneity.This work presents methods for haptic modelling of soft and hard tissue with varying stiffness. The model provides visualization of deformation and calculates force feedback during simulated epidural needle insertion. A springmassdamper (SMD) network is configured from magnetic resonance image (MRI) slices of patient’s lumbar region to represent varying stiffness throughout tissue structure. Reaction force is calculated from the SMD network and a haptic device is configured to produce a needle insertion simulation. The user can feel the changing forces as the needle is inserted through tissue layers and ligaments. Methods for calculating the force feedback at various depths of needle insertion are presented. Voxelization is used to fill ligament surface meshes with spring mass damper assemblies for simulated needle insertion into soft and hard tissues. Modelled vertebrae cannot be pierced by the needle. Graphs were produced during simulated needle insertions to compare the applied force to haptic reaction force. Preliminary saline pressure measurements during Tuohy epidural needle insertion are also used as a basis for forces generated in the simulation.

High order algorithms for numerical solution of fractional differential equationsIn this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.

A high order numerical method for solving nonlinear fractional differential equation with nonuniform meshesWe 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.

High performing AgNW transparent conducting electrodes with a sheet resistance of 2.5 Ω Sq−1 based upon a rolltoroll compatible postprocessing techniqueThe 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.

High speed CO2 laser surface modification of iron/cobalt codoped boroaluminosilicate glassA preliminary study into the impact of high speed laser processing on the surface of iron and cobalt codoped glass substrates using a 60 W continuous wave (cw) CO2 laser. Two types of processing, termed fillprocessing and lineprocessing, were trialled. In fillprocessed samples the surface roughness of the glass was found to increase linearly with laser power from an Sa value of 20.8 nm–2.1 μm at a processing power of 54 W. With line processing, a more exponentiallike increase was observed with a roughness of 4 μm at 54 W. The change in surface properties of the glass, such as gloss and wettability, have also been measured. The contact angle of water was found to increase after laser processing by up to 64°. The surface gloss was varied between 45 and 100 gloss units (GUs).

High temperature performance of a piezoelectric micro cantilever for vibration energy harvestingEnergy harvesters withstanding high temperatures could provide potentially unlimited energy to sensor nodes placed in harsh environments, where manual maintenance is difficult and costly. Experimental results on a classical microcantilever show a 67% drop of the maximum power when the temperature is increased up to 160 °C. This decrease is investigated using a lumpedparameters model which takes into account variations in material parameters with temperature, damping increase and thermal stresses induced by mismatched thermal coefficients in a composite cantilever. The model allows a description of the maximum power evolution as a function of temperature and input acceleration. Simulation results further show that an increase in damping and the apparition of thermal stresses are contributing to the power drop at 59% and 13% respectively.

HighOrder Numerical Methods for Solving Time Fractional Partial Differential EquationsIn this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm’s method where the Hadamard finitepart integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order O(τ^(3−α) +h^2 ),0

A highorder scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equationA new highorder finite difference scheme to approximate the Caputo fractional derivative $\frac{1}{2} \big ( \, _{0}^{C}D^{\alpha}_{t}f(t_{k})+ \, _{0}^{C}D^{\alpha}_{t}f(t_{k1}) \big ), k=1, 2, \dots, N, $ with the convergence order $O(\Delta t^{4\alpha}), \, \alpha\in(1,2)$ is obtained when $f^{\prime \prime \prime} (t_{0})=0$, where $\Delta t$ denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order $O(\Delta t^{4\alpha} + h^2)$, where $h$ denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

A higher order numerical method for time fractional partial differential equations with nonsmooth dataGao et al. (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate $O(k^{3\alpha}), 0< \alpha <1$ by directly approximating the integerorder derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu (2016), where $k$ is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate $O(k^{3\alpha}), 0< \alpha <1$ uniformly with respect to the time variable $t$. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate $O(k^{3 \alpha}), 0 < \alpha <1$ uniformly with respect to the time variable $t$. In this paper, we first obtain a similar approximation scheme to the RiemannLiouville fractional derivative with the convergence rate $O(k^{3 \alpha}), 0 < \alpha <1$ as in Gao \et \cite{gaosunzha} (2014) by approximating the Hadamard finitepart integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate $O(k^{3 \alpha}), 0 < \alpha <1$ for any fixed $t_{n}>0$ for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Higher Order Numerical Methods for Fractional Order Differential EquationsThis thesis explores higher order numerical methods for solving fractional differential equations.

Higher order numerical methods for solving fractional differential equationsIn this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is O(h^(3−α)). Our second approach is based on discretisation of the integral form of the fractional differential equation and we obtain a fractional Adamstype method for a nonlinear fractional differential equation of any order α >0. The order of convergence of the numerical method is O(h^3) for α ≥ 1 and O(h^(1+2α)) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

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.

High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problemWe use the generalized L1 approximation for the Caputo fractional derivative, the secondorder fractional quadrature rule approximation for the integral term, and a classical CrankNicolson alternating direction implicit (ADI)scheme for the time discretization of a new twodimensional (2D) fractionalintegrodifferential equation, in combination with a space discretization by anarbitraryorder orthogonal spline collocation (OSC) method. The stability of aCrankNicolson ADI OSC scheme is rigourously established, and error estimateis also derived. Finally, some numerical tests are given

How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation?This paper discusses the numerical solution of delay differential equations undergoing a Hopf birufication. Three distinct and complementary approaches to the analysis are presented.

How effective is Ant Colony Optimisation at Robot Path PlanningThis project involves investigation of the problem robot path planning using ant colony optimisation heuristics to construct the quickest path from the starting point to the end. The project has developed a simulation that successfully simulates as well as demonstrates visually through a graphical user interface, robot path planning using ant colony optimisation. The simulation shows an ability to traverse an unknown environment from a start point to an end and successfully construct a route for others to follow both when the terrain is dynamic and static