Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

Mild systemic hypoxia and photopic visual field sensitivity

Purpose: Flickering stimuli increase the metabolic demand of the retina,making it a sensitive perimetric stimulus to the early onset of retinal disease. We determine whether flickering stimuli are a sensitive indicator of vision deficits resulting from to acute, mild systemic hypoxia when compared to standard static perimetry. Methods: Static and flicker visual perimetry were performed in 14 healthy young participants while breathing 12% oxygen (hypoxia) under photopic illumination. The hypoxia visual field data were compared with the field data measured during normoxia. Absolute sensitivities (in dB) were analysed in seven concentric rings at 1°, 3°, 6°, 10°, 15°, 22° and 30° eccentricities as well as mean defect (MD) and pattern defect (PD) were calculated. Preliminary data are reported for mesopic light levels. Results: Under photopic illumination, flicker and static visual field sensitivities at all eccentricities were not significantly different between hypoxia and normoxia conditions. The mean defect and pattern defect were not significantly different for either test between the two oxygenation conditions. Conclusion: Although flicker stimulation increases cellular metabolism, flicker photopic visual field impairment is not detected during mild hypoxia. These findings contrast with electrophysiological flicker tests in young participants that show impairment at photopic illumination during the same levels of mild hypoxia. Potential mechanisms contributing to the difference between the visual fields and electrophysiological flicker tests including variability in perimetric data, neuronal adaptation and vascular autoregulation, are considered. The data have implications for the use of visual perimetry in the detection of ischaemic/hypoxic retinal disorders under photopic and mesopic light levels.

Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Tracking employees’ twists and turns : a mixed methods approach to assessing change in the psychological contract

The psychological contract has emerged over the past 60 years as a key analytical device for both academics and practitioners to conceptualise and explain the employment relationship. However, despite the recognised import of this field, some authors suggest it has fallen into a ‘methodological rut’ and is neglecting to empirically assess basic theoretical tenets of the concept – such as the temporal and individualised, subjective nature of the construct. This paper describes the research design of a longitudinal, mixed methods study to explore development and change in the psychological contract and outline how the use of individual growth modelling can be a powerful tool in analysing the type of quantitative data collected. Finally, by briefly outlining the benefits of this approach, the paper seeks to offer an alternative methodology to explore the dynamic and intra-individual processes within the psychological contract domain.

Visual field size criteria for mobility rehabilitation referral

Purpose. To investigate evidence-based visual field size criteria for referral of low-vision (LV) patients for mobility rehabilitation. Methods. One hundred and nine participants with LV and 41 age-matched participants with normal sight (NS) were recruited. The LV group was heterogeneous with diverse causes of visual impairment. We measured binocular kinetic visual fields with the Humphrey Field Analyzer and mobility performance on an obstacle-rich, indoor course. Mobility was assessed as percent preferred walking speed (PPWS) and number of obstacle-contact errors. The weighted kappa coefficient of association (κr) was used to discriminate LV participants with both unsafe and inefficient mobility from those with adequate mobility on the basis of their visual field size for the full sample and for subgroups according to type of visual field loss and whether or not the participants had previously received orientation and mobility training. Results. LV participants with both PPWS <38% and errors >6 on our course were classified as having inadequate (inefficient and unsafe) mobility compared with NS participants. Mobility appeared to be first compromised when the visual field was less than about 1.2 steradians (sr; solid angle of a circular visual field of about 70° diameter). Visual fields <0.23 and 0.63 sr (31 to 52° diameter) discriminated patients with at-risk mobility for the full sample and across the two subgroups. A visual field of 0.05 sr (15° diameter) discriminated those with critical mobility. Conclusions. Our study suggests that: practitioners should be alert to potential mobility difficulties when the visual field is less than about 1.2 sr (70° diameter); assessment for mobility rehabilitation may be warranted when the visual field is constricted to about 0.23 to 0.63 sr (31 to 52° diameter) depending on the nature of their visual field loss and previous history (at risk); and mobility rehabilitation should be conducted before the visual field is constricted to 0.05 sr (15° diameter; critical).

Evaluating Two Mass Screening Methods for Tungro Disease Resistance

Tungro is one of the most destructive viral diseases of rice in South and Southeast Asia. It is associated with two viruses---rice tungro bacilliform virus (RTBV) ,and rice tungro spherical virus (RTSV) (Hibino et al 1978). Both viruses are transmitted by the green leafhopper (GLH) Nephotettix virescens (Ling 1979), However, prior acquisition of RTSV is required for Ihe transmission of RTBV alone (Hibino 1983). Plants infected with both viruses show severe stunting and yellowing. Those infected with RTBV alone show mild stunting but no leaf discoloration whereas those infected with RTSV alone do not show any apparent symptoms (Hibino el al 1978). Since the late 1960s, tungro has been mainly managed through varietal resistance (Khush 1989). The instability of resistant varieties in the field (Dahal et .a1 1990) led to a reexamination of the nature of the incorporated sources of resistance and to the adoption of more precise and more accurate screening methods.

Getting lost in the field : the unpredictable nature of fieldwork with young people

This chapter focuses on the unpredictable nature of fieldwork with young offenders, specifically with those in a marginalised context. We begin by recounting our experiences working with young people who have had contact with criminal justice processes, particularly those who are the subject of extreme levels of official social control. We then turn to a discussion of the challenges associated with the unpredictable nature of fieldwork, specifically the difficulties associated with negotiating access with gatekeepers and negotiating with young people. We also discuss specific challenges with the research ethics governance of ethically sensitive research in this context (e.g. interviewing young people about offending behaviour). Finally, we recount our experiences in working these young people, with a focus on ‘the grunt’: that is, drawing out young peoples’ stories in interviews. We conclude with some reflections on the need to develop systematic instruction in qualitative work in this specific context.

Inferior visual field reductions are associated with poorer functional status among older adults with glaucoma

Purpose: To examine the relationship between visual impairment and functional status in a community-dwelling sample of older adults with glaucoma. Methods: This study included 74 community-dwelling older adults with open-angle glaucoma (aged 74 ± 6 years). Assessment of central vision included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from merged monocular Humphrey Field Analyser visual field plots. Functional status outcome measures included physical performance tests (6-min walk test, timed up and go test and lower limb strength), a physical activity questionnaire (Physical Activity Scale for the Elderly) and an overall functional status score. Correlation and linear regression analyses, adjusting for age and gender, examined the association between visual impairment and functional status outcomes. Results: Greater levels of visual impairment were significantly associated with lower levels of functional status among community-dwelling older adults with glaucoma, independent of age and gender. Specifically, lower levels of visual function were associated with slower timed up and go performance, weaker lower limb strength, lower self-reported physical activity, and lower overall functional status scores. Of the components of vision examined, the inferior visual field and contrast factors were the strongest predictors of these functional outcomes, whereas the superior visual field factor was not related to functional status. Conclusions: Greater visual impairment, particularly in the inferior visual field and loss of contrast sensitivity, was associated with poorer functional status among older adults with glaucoma. The findings of this study highlight the potential links between visual impairment and the onset of functional decline. Interventions which promote physical activity among older adults with glaucoma may assist in preventing functional decline, frailty and falls, and improve overall health and well-being.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Development and validation of novel methods for microbial source tracking based on Escherichia coli as an indicator of water quality

Microbial pollution in water periodically affects human health in Australia, particularly in times of drought and flood. There is an increasing need for the control of waterborn microbial pathogens. Methods, allowing the determination of the origin of faecal contamination in water, are generally referred to as Microbial Source Tracking (MST). Various approaches have been evaluated as indicatorsof microbial pathogens in water samples, including detection of different microorganisms and various host-specific markers. However, until today there have been no universal MST methods that could reliably determine the source (human or animal) of faecal contamination. Therefore, the use of multiple approaches is frequently advised. MST is currently recognised as a research tool, rather than something to be included in routine practices. The main focus of this research was to develop novel and universally applicable methods to meet the demands for MST methods in routine testing of water samples. Escherichia coli was chosen initially as the object organism for our studies as, historically and globally, it is the standard indicator of microbial contamination in water. In this thesis, three approaches are described: single nucleotide polymorphism (SNP) genotyping, clustered regularly interspaced short palindromic repeats (CRISPR) screening using high resolution melt analysis (HRMA) methods and phage detection development based on CRISPR types. The advantage of the combination SNP genotyping and CRISPR genes has been discussed in this study. For the first time, a highly discriminatory single nucleotide polymorphism interrogation of E. coli population was applied to identify the host-specific cluster. Six human and one animal-specific SNP profile were revealed. SNP genotyping was successfully applied in the field investigations of the Coomera watershed, South-East Queensland, Australia. Four human profiles [11], [29], [32] and [45] and animal specific SNP profile [7] were detected in water. Two human-specific profiles [29] and [11] were found to be prevalent in the samples over a time period of years. The rainfall (24 and 72 hours), tide height and time, general land use (rural, suburban), seasons, distance from the river mouth and salinity show a lack of relashionship with the diversity of SNP profiles present in the Coomera watershed (p values > 0.05). Nevertheless, SNP genotyping method is able to identify and distinquish between human- and non-human specific E. coli isolates in water sources within one day. In some samples, only mixed profiles were detected. To further investigate host-specificity in these mixed profiles CRISPR screening protocol was developed, to be used on the set of E. coli, previously analysed for SNP profiles. CRISPR loci, which are the pattern of previous DNA coliphages attacks, were considered to be a promising tool for detecting host-specific markers in E. coli. Spacers in CRISPR loci could also reveal the dynamics of virulence in E. coli as well in other pathogens in water. Despite the fact that host-specificity was not observed in the set of E. coli analysed, CRISPR alleles were shown to be useful in detection of the geographical site of sources. HRMA allows determination of ‘different’ and ‘same’ CRISPR alleles and can be introduced in water monitoring as a cost-effective and rapid method. Overall, we show that the identified human specific SNP profiles [11], [29], [32] and [45] can be useful as marker genotypes globally for identification of human faecal contamination in water. Developed in the current study, the SNP typing approach can be used in water monitoring laboratories as an inexpensive, high-throughput and easy adapted protocol. The unique approach based on E. coli spacers for the search for unknown phage was developed to examine the host-specifity in phage sequences. Preliminary experiments on the recombinant plasmids showed the possibility of using this method for recovering phage sequences. Future studies will determine the host-specificity of DNA phage genotyping as soon as first reliable sequences can be acquired. No doubt, only implication of multiple approaches in MST will allow identification of the character of microbial contamination with higher confidence and readability.

Prediction of structural integrity, robustness and service life using advanced finite element methods

Corrosion is a common phenomenon and critical aspects of steel structural application. It affects the daily design, inspection and maintenance in structural engineering, especially for the heavy and complex industrial applications, where the steel structures are subjected to hash corrosive environments in combination of high working stress condition and often in open field and/or under high temperature production environments. In the paper, it presents the actual engineering application of advanced finite element methods in the predication of the structural integrity and robustness at a designed service life for the furnaces of alumina production, which was operated in the high temperature, corrosive environments and rotating with high working stress condition.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

Comparing cost uplift in infrastructure delivery methods : a case based approach

In 2009 the Australian Federal and State governments are expected to have spent some AU$30 billion procuring infrastructure projects. For governments with finite resources but many competing projects, formal capital rationing is achieved through use of Business Cases. These Business cases articulate the merits of investing in particular projects along with the estimated costs and risks of each project. Despite the sheer size and impact of infrastructure projects, there is very little research in Australia, or internationally, on the performance of these projects against Business Case assumptions when the decision to invest is made. If such assumptions (particularly cost assumptions) are not met, then there is serious potential for the misallocation of Australia’s finite financial resources. This research addresses this important gap in the literature by using combined quantitative and qualitative research methods, to examine the actual performance of 14 major Australian government infrastructure projects. The research findings are controversial as they challenge widely held perceptions of the effectiveness of certain infrastructure delivery practices. Despite this controversy, the research has had a significant impact on the field and has been described as ‘outstanding’ and ‘definitive’ (Alliancing Association of Australasia), "one of the first of its kind" (Infrastructure Partnerships of Australia) and "making a critical difference to infrastructure procurement" (Victorian Department of Treasury). The implications for practice of the research have been profound and included the withdrawal by Government of various infrastructure procurement guidelines, the formulation of new infrastructure policies by several state governments and the preparation of new infrastructure guidelines that substantially reflect the research findings. Building on the practical research, a more rigorous academic investigation focussed on the comparative cost uplift of various project delivery strategies was submitted to Australia’s premier academic management conference, the Australian and New Zealand Academy of Management (ANZAM) Annual Conference. This paper has been accepted for the 2010 ANZAM National Conference following a process of double blind peer review with reviewers rating the paper’s overall contribution as "Excellent" and "Good".

Towards participatory action design research : adapting action research and design science research methods for urban informatics

This paper proposes a new research method, Participatory Action Design Research (PADR), for studies in the Urban Informatics domain. PADR supports Urban Informatics research in developing new technological means (e.g. using mobile and ubiquitous computing) to resolve contemporary issues or support everyday life in urban environments. The paper discusses the nature, aims and inherent methodological needs of Urban Informatics research, and proposes PADR as a method to address these needs. Situated in a socio-technical context, Urban Informatics requires a close dialogue between social and design-oriented fields of research as well as their methods. PADR combines Action Research and Design Science Research, both of which are used in Information Systems, another field with a strong socio-technical emphasis, and further adapts them to the cross-disciplinary needs and research context of Urban Informatics.