Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

Fast exact nearest neighbour matching in high dimensions using d-D Sort

Data structures such as k-D trees and hierarchical k-means trees perform very well in approximate k nearest neighbour matching, but are only marginally more effective than linear search when performing exact matching in high-dimensional image descriptor data. This paper presents several improvements to linear search that allows it to outperform existing methods and recommends two approaches to exact matching. The first method reduces the number of operations by evaluating the distance measure in order of significance of the query dimensions and terminating when the partial distance exceeds the search threshold. This method does not require preprocessing and significantly outperforms existing methods. The second method improves query speed further by presorting the data using a data structure called d-D sort. The order information is used as a priority queue to reduce the time taken to find the exact match and to restrict the range of data searched. Construction of the d-D sort structure is very simple to implement, does not require any parameter tuning, and requires significantly less time than the best-performing tree structure, and data can be added to the structure relatively efficiently.

Accuracy and functional variability in elite and developing fast bowlers

Objectives The relationship between performance variability and accuracy in cricket fast bowlers of different skill levels under three different task conditions was investigated. Bowlers of different skill levels were examined to observe if they could adapt movement patterns to maintain performance accuracy on a bowling skills test. Design 8 national, 12 emerging and 12 junior pace bowlers completed an adapted version of the Cricket Australia bowling skills test, in which they performed 30 trials involving short (n = 10), good (n = 10), and full (n = 10) length deliveries. Methods Bowling accuracy was recorded by digitising ball position relative to the centre of a target. Performance measures were mean radial error (accuracy), variable error (consistency), centroid error (bias), bowling score and ball speed. Radial error changes across the duration of the skills test were used to record accuracy adjustment in subsequent deliveries. Results Elite fast bowlers performed better in speed, accuracy, and test scores than developing athletes. Bowlers who were less variable were also more accurate across all delivery lengths. National and emerging bowlers were able to adapt subsequent performance trials within the same bowling session for short length deliveries. Conclusions Accuracy and adaptive variability were key components of elite performance in fast bowling which improved with skill level. In this study, only national elite bowlers showed requisite levels of adaptive variability to bowl a range of lengths to different pitch locations.

The water catchment : fast forward to the past

The Water Catchment: fast forward to the past comprises two parts: a creative piece and an exegesis. The methodology is Creative Practice as Research; a process of critical reflection, where I observe how researching the exegesis, in my case analysing how the social reality of an era in which an author writes affects their writing of the protagonist's journey, and how this in turn shapes how I write the hero's pathway in the creative piece. The genre in which the protagonist's journey is charted and represented is dystopian young adult fiction; hence my creative piece, The Water Catchment, is a novel manuscript for a dystopian young adult fantasy. It is a speculative novel set in a possible future and poses (and answers) the question: What might happen if water becomes the most powerful commodity on earth? There are two communities, called 'worlds' to create a barrier and difference where physical ones are not in evidence. A battle ensues over unfair conditions and access to water. In the end the protagonist, Caitlyn, takes over leadership heralding a new era of co-operation and water management between the two worlds. The exegesis examines how the hero's pathway, the journey towards knowledge and resolution, is best explored in young adult literature through dystopian narratives. I explore how the dystopian worlds of Ursula Le Guin's first and last books of The Earthsea Quartet are foundational, and lay this examination over an analysis of both the hero's pathway within and the social contexts outside of the novels. Dystopian narratives constitute a liberating space for the adolescent protagonist between the reliance on adults in childhood and the world of adults. In young adult literature such narratives provide fertile ground to explore those aspects informing an adolescent's future.

Reconstructing 3D x-ray CT images of polymer gel dosimeters using the zero-scan method

In this study x-ray CT has been used to produce a 3D image of an irradiated PAGAT gel sample, with noise-reduction achieved using the ‘zero-scan’ method. The gel was repeatedly CT scanned and a linear fit to the varying Hounsfield unit of each pixel in the 3D volume was evaluated across the repeated scans, allowing a zero-scan extrapolation of the image to be obtained. To minimise heating of the CT scanner’s x-ray tube, this study used a large slice thickness (1 cm), to provide image slices across the irradiated region of the gel, and a relatively small number of CT scans (63), to extrapolate the zero-scan image. The resulting set of transverse images shows reduced noise compared to images from the initial CT scan of the gel, without being degraded by the additional radiation dose delivered to the gel during the repeated scanning. The full, 3D image of the gel has a low spatial resolution in the longitudinal direction, due to the selected scan parameters. Nonetheless, important features of the dose distribution are apparent in the 3D x-ray CT scan of the gel. The results of this study demonstrate that the zero-scan extrapolation method can be applied to the reconstruction of multiple x-ray CT slices, to provide useful 2D and 3D images of irradiated dosimetry gels.

Fast formulas for computing cryptographic pairings

The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option. This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond. This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

Mg-based nanocomposites with high capacity and fast kinetics for hydrogen storage

Magnesium and its alloys have shown a great potential in effective hydrogen storage due to their advantages of high volumetric/gravimetric hydrogen storage capacity and low cost. However, the use of these materials in fuel cells for automotive applications at the present time is limited by high hydrogenation temperature and sluggish sorption kinetics. This paper presents the recent results of design and development of magnesium-based nanocomposites demonstrating the catalytic effects of carbon nanotubes and transition metals on hydrogen adsorption in these materials. The results are promising for the application of magnesium materials for hydrogen storage, with significantly reduced absorption temperatures and enhanced ab/desorption kinetics. High level Density Functional Theory calculations support the analysis of the hydrogenation mechanisms by revealing the detailed atomic and molecular interactions that underpin the catalytic roles of incorporated carbon and titanium, providing clear guidance for further design and development of such materials with better hydrogen storage properties.

An X chromosome association scan of the Norfolk Island genetic isolate provides evidence for a novel migraine susceptibility locus at Xq12

Migraine is a common and debilitating neurovascular disorder with a complex envirogenomic aetiology. Numerous studies have demonstrated a preponderance of women affected with migraine and previous pedigree linkage studies in our laboratory have identified susceptibility loci on chromosome Xq24-Xq28. In this study we have used the genetic isolate of Norfolk Island to further analyse the X chromosome for migraine susceptibility loci. An association approach was employed to analyse 14,124 SNPs spanning the entire X chromosome. Genotype data from 288 individuals comprising a large core-pedigree, of which 76 were affected with migraine, were analysed. Although no SNP reached chromosome-wide significance (empirical α = 1×10−5) ranking by P-value revealed two primary clusters of SNPs in the top 25. A 10 SNP cluster represents a novel migraine susceptibility locus at Xq12 whilst a 11 SNP cluster represents a previously identified migraine susceptibility locus at Xq27. The strongest association at Xq12 was seen for rs599958 (OR = 1.75, P = 8.92×10−4), whilst at Xq27 the strongest association was for rs6525667 (OR = 1.53, P = 1.65×10−4). Further analysis of SNPs at these loci was performed in 5,122 migraineurs from the Women’s Genome Health Study and provided additional evidence for association at the novel Xq12 locus (P<0.05). Overall, this study provides evidence for a novel migraine susceptibility locus on Xq12. The strongest effect SNP (rs102834, joint P = 1.63×10−5) is located within the 5′UTR of the HEPH gene, which is involved in iron homeostasis in the brain and may represent a novel pathway for involvement in migraine pathogenesis.

A genome-wide scan provides evidence for loci influencing a severe heritable form of common migraine

Migraine is a prevalent neurovascular disease with a significant genetic component. Linkage studies have so far identified migraine susceptibility loci on chromosomes 1, 4, 6, 11, 14, 19 and X. We performed a genome-wide scan of 92 Australian pedigrees phenotyped for migraine with and without aura and for a more heritable form of “severe” migraine. Multipoint non-parametric linkage analysis revealed suggestive linkage on chromosome 18p11 for the severe migraine phenotype (LOD*=2.32, P=0.0006) and chromosome 3q (LOD*=2.28, P=0.0006). Excess allele sharing was also observed at multiple different chromosomal regions, some of which overlap with, or are directly adjacent to, previously implicated migraine susceptibility regions. We have provided evidence for two loci involved in severe migraine susceptibility and conclude that dissection of the “migraine” phenotype may be helpful for identifying susceptibility genes that influence the more heritable clinical (symptom) profiles in affected pedigrees. Also, we concluded that the genetic aetiology of the common (International Headache Society) forms of the disease is probably comprised of a number of low to moderate effect susceptibility genes, perhaps acting synergistically, and this effect is not easily detected by traditional single-locus linkage analyses of large samples of affected pedigrees.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Higher harmonic large-amplitude fourier transformed alternating current voltammetry : analytical attributes derived from studies of the oxidation of ferrocenemethanol and uric acid at a glassy carbon electrode

An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s−1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e− rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast.

Morphology changes and mechanistic aspects of the electrochemically-induced reversible solid-solid transformation of microcrystalline TCNQ into Co TCNQ 2-based materials (TCNQ= 7, 7, 8, 8-Tetracyanoquinodimethane)

The chemically reversible solid−solid phase transformation of a TCNQ-modified glassy carbon, indium tin oxide, or metal electrode into Co\[TCNQ]2(H2O)2 material in the presence of Co2+(aq) containing electrolytes has been induced and monitored electrochemically. Voltammetric data reveal that the TCNQ/Co\[TCNQ]2(H2O)2 interconversion process is independent of electrode material and identity of cobalt electrolyte anion. However, a marked dependence on electrolyte concentration, scan rate, and method of electrode modification (drop casting or mechanical attachment) is found. Cyclic voltammetric and double potential step chronoamperometric measurements confirm that formation of Co\[TCNQ]2(H2O)2 occurs through a rate-determining nucleation and growth process that initially involves incorporation of Co2+(aq) ions into the reduced TCNQ crystal lattice at the TCNQ|electrode|electrolyte interface. Similarly, the reverse (oxidation) process, which involves transformation of solid Co\[TCNQ]2(H2O)2 back to parent TCNQ crystals, also is controlled by nucleation−growth kinetics. The overall chemically reversible process that represents this transformation is described by the reaction:  2TCNQ0(s) + 2e- + Co2+(aq) + 2H2O \[Co(TCNQ)2(H2O)2](s). Ex situ SEM images illustrated that this reversible TCNQ/Co\[TCNQ]2(H2O)2 conversion process is accompanied by drastic size and morphology changes in the parent solid TCNQ. In addition, different sizes of needle-shaped nanorod/nanowire crystals of Co\[TCNQ]2(H2O)2 are formed depending on the method of surface immobilization.

Voltammetric monitoring of gold nanoparticle formation facilitated by glycyl-L-tyrosine : relation to electronic spectra and transmission electron microscopy images

Voltammetric techniques have been introduced to monitor the formation of gold nanoparticles produced via the reaction of the amino acid glycyl-L-tyrosine with Au(III) (bromoaurate) in 0.05 M KOH conditions. The alkaline conditions facilitate amino acid binding to Au(III), inhibit the rate of reduction to Au(0), and provide an excellent supporting electrolyte for voltammetric studies. Data obtained revealed that a range of time-dependent gold solution species are involved in gold nanoparticle formation and that the order in which reagents are mixed is critical to the outcome. Concomitantly with voltammetric measurements, the properties of gold nanoparticles formed are probed by examination of electronic spectra in order to understand how the solution environment present during nanoparticle growth affects the final distribution of the nanoparticles. Images obtained by the ex situ transmission electron microscopy (TEM) technique enable the physical properties of the nanoparticles isolated in the solid state to be assessed. Use of this combination of in situ and ex situ techniques provides a versatile framework for elucidating the details of nanoparticle formation.

Electrochemically-induced TCNQ/Mn TCNQ 2 (H2O) 2 (TCNQ= 7, 7, 8, 8-Tetracyanoquinodimethane) solid-solid interconversion : two voltammetrically distinct processes that allow selective generation of nanofiber or nanorod network morphologies

Unlike the case with other divalent transition metal M\[TCNQ](2)(H(2)O)(2) (M = Fe, Co, Ni) analogues, the electrochemically induced solid-solid phase interconversion of TCNQ microcrystals (TCNQ = 7,7,8,8-tetracyanoquinodimethane) to Mn\[TCNQ](2)(H(2)O)(2) occurs via two voltammetrically distinct, time dependent processes that generate the coordination polymer in nanofiber or rod-like morphologies. Careful manipulation of the voltammetric scan rate, electrolysis time, Mn(2+)((aq)) concentration, and the method of electrode modification with solid TCNQ allows selective generation of either morphology. Detailed ex situ spectroscopic (IR, Raman), scanning electron microscopy (SEM), and X-ray powder diffraction (XRD) characterization clearly establish that differences in the electrochemically synthesized Mn-TCNQ material are confined to morphology. Generation of the nanofiber form is proposed to take place rapidly via formation and reduction of a Mn-stabilized anionic dimer intermediate, \[(Mn(2+))(TCNQ-TCNQ)(2)(*-)], formed as a result of radical-substrate coupling between TCNQ(*-) and neutral TCNQ, accompanied by ingress of Mn(2+) ions from the aqueous solution at the triple phase TCNQ/electrode/electrolyte boundary. In contrast, formation of the nanorod form is much slower and is postulated to arise from disproportionation of the \[(Mn(2+))(TCNQ-TCNQ)(*-)(2)] intermediate. Thus, identification of the time dependent pathways via the solid-solid state electrochemical approach allows the crystal size of the Mn\[TCNQ](2)(H(2)O)(2) material to be tuned and provides new mechanistic insights into the formation of different morphologies.