Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Comprehensive standardized data definitions for acute coronary syndrome research in emergency departments in Australasia

Patients with chest discomfort or other symptoms suggestive of acute coronary syndrome (ACS) are one of the most common categories seen in many Emergency Departments (EDs). While the recognition of patients at high-risk of ACS has improved steadily, identifying the majority of chest pain presentations who fall into the low-risk group remains a challenge. Research in this area needs to be transparent, robust, applicable to all hospitals from large tertiary centres to rural and remote sites, and to allow direct comparison between different studies with minimum patient spectrum bias. A standardised approach to the research framework using a common language for data definitions must be adopted to achieve this. The aim was to create a common framework for a standardised data definitions set that would allow maximum value when extrapolating research findings both within Australasian ED practice, and across similar populations worldwide. Therefore a comprehensive data definitions set for the investigation of non-traumatic chest pain patients with possible ACS was developed, specifically for use in the ED setting. This standardised data definitions set will facilitate ‘knowledge translation’ by allowing extrapolation of useful findings into the real-life practice of emergency medicine.

A randomised controlled trial of a tele-based lifestyle intervention for colorectal cancer survivors ('CanChange') : Study protocol

Background Colorectal cancer survivors may suffer from a range of ongoing psychosocial and physical problems that negatively impact on quality of life. This paper presents the study protocol for a novel telephone-delivered intervention to improve lifestyle factors and health outcomes for colorectal cancer survivors. Methods/Design Approximately 350 recently diagnosed colorectal cancer survivors will be recruited through the Queensland Cancer Registry and randomised to the intervention or control condition. The intervention focuses on symptom management, lifestyle and psychosocial support to assist participants to make improvements in lifestyle factors (physical activity, healthy diet, weight management, and smoking cessation) and health outcomes. Participants will receive up to 11 telephone-delivered sessions over a 6 month period from a qualified health professional or 'health coach'. Data collection will occur at baseline (Time 1), post-intervention or six months follow-up (Time 2), and at 12 months follow-up for longer term effects (Time 3). Primary outcome measures will include physical activity, cancer-related fatigue and quality of life. A cost-effective analysis of the costs and outcomes for survivors in the intervention and control conditions will be conducted from the perspective of health care costs to the government. Discussion The study will provide valuable information about an innovative intervention to improve lifestyle factors and health outcomes for colorectal cancer survivors.

Studies of the radiation chemistry and grafting of a fluoropolymer

The radiation chemistry and the grafting of a fluoropolymer, poly(tetrafluoroethylene-coperfluoropropyl vinyl ether) (PFA), was investigated with the aim of developing a highly stable grafted support for use in solid phase organic chemistry (SPOC). A radiation-induced grafting method was used whereby the PFA was exposed to ionizing radiation to form free radicals capable of initiating graft copolymerization of styrene. To fully investigate this process, both the radiation chemistry of PFA and the grafting of styrene to PFA were examined. Radiation alone was found to have a detrimental effect on PFA when irradiated at 303 K. This was evident from the loss in the mechanical properties due to chain scission reactions. This meant that when radiation was used for the grafting reactions, the total radiation dose needed to be kept as low as possible. The radicals produced when PFA was exposed to radiation were examined using electron spin resonance spectroscopy. Both main-chain (–CF2–C.F–CF2-) and end-chain (–CF2–C.F2) radicals were identified. The stability of the majority of the main-chain radicals when the polymer was heated above the glass transition temperature suggested that they were present mainly in the crystalline regions of the polymer, while the end-chain radicals were predominately located in the amorphous regions. The radical yield at 77 K was lower than the radical yield at 303 K suggesting that cage recombination at low temperatures inhibited free radicals from stabilizing. High-speed MAS 19F NMR was used to identify the non-volatile products after irradiation of PFA over a wide temperature range. The major products observed over the irradiation temperature 303 to 633 K included new saturated chain ends, short fluoromethyl side chains in both the amorphous and crystalline regions, and long branch points. The proportion of the radiolytic products shifted from mainly chain scission products at low irradiation temperatures to extensive branching at higher irradiation temperatures. Calculations of G values revealed that net crosslinking only occurred when PFA was irradiated in the melt. Minor products after irradiation at elevated temperatures included internal and terminal double bonds and CF3 groups adjacent to double bonds. The volatile products after irradiation at 303 K included tetrafluoromethane (CF4) and oxygen-containing species from loss of the perfluoropropyl ether side chains of PFA as identified by mass spectrometry and FTIR spectroscopy. The chemical changes induced by radiation exposure were accompanied by changes in the thermal properties of the polymer. Changes in the crystallinity and thermal stability of PFA after irradiation were examined using DSC and TGA techniques. The equilibrium melting temperature of untreated PFA was 599 K as determined using a method of extrapolation of the melting temperatures of imperfectly formed crystals. After low temperature irradiation, radiation- induced crystallization was prevalent due to scission of strained tie molecules, loss of perfluoropropyl ether side chains, and lowering of the molecular weight which promoted chain alignment and hence higher crystallinity. After irradiation at high temperatures, the presence of short and long branches hindered crystallization, lowering the overall crystallinity. The thermal stability of the PFA decreased with increasing radiation dose and temperature due to the introduction of defect groups. Styrene was graft copolymerized to PFA using -radiation as the initiation source with the aim of preparing a graft copolymer suitable as a support for SPOC. Various grafting conditions were studied, such as the total dose, dose rate, solvent effects and addition of nitroxides to create “living” graft chains. The effect of dose rate was examined when grafting styrene vapour to PFA using the simultaneous grafting method. The initial rate of grafting was found to be independent of the dose rate which implied that the reaction was diffusion controlled. When the styrene was dissolved in various solvents for the grafting reaction, the graft yield was strongly dependent of the type and concentration of the solvent used. The greatest graft yield was observed when the solvent swelled the grafted layers and the substrate. Microprobe Raman spectroscopy was used to map the penetration of the graft into the substrate. The grafted layer was found to contain both poly(styrene) (PS) and PFA and became thicker with increasing radiation dose and graft yield which showed that grafting began at the surface and progressively penetrated the substrate as the grafted layer was swollen. The molecular weight of the grafted PS was estimated by measuring the molecular weight of the non-covalently bonded homopolymer formed in the grafted layers using SEC. The molecular weight of the occluded homopolymer was an order of magnitude greater than the free homopolymer formed in the surrounding solution suggesting that the high viscosity in the grafted regions led to long PS grafts. When a nitroxide mediated free radical polymerization was used, grafting occurred within the substrate and not on the surface due to diffusion of styrene into the substrate at the high temperatures needed for the reaction to proceed. Loading tests were used to measure the capacity of the PS graft to be functionialized with aminomethyl groups then further derivatized. These loading tests showed that samples grafted in a solution of styrene and methanol had superior loading capacity over samples graft using other solvents due to the shallow penetration and hence better accessibility of the graft when methanol was used as a solvent.

A life jacket with holes- : a case study of 'temporary engagement' : a strategy used by Education Queensland to employ beginning secondary teachers

This research investigated the impact of Education Queensland's employment policy and practices for beginning secondary teachers appointed on temporary engagement. The context was the public secondary school sector within the state of Queensland, Australia. The study was set within a context of the changing nature of work from full-time permanent employment towards casual, fixed-term contracts, temporary and part-time employment, a trend reflected in the employment patterns for teachers within Australia. Two broad categories of literature relating to the research problem of this thesis were reviewed, namely the beginning teacher and permanency or tenure. The focus in the research literature on beginning teachers was the professional experiences of teachers within the classroom and school. There was a paucity of research that considered the working and industrial conditions of temporary employment for beginning teachers or the personal and professional implications of this form of employment. The review of the context and literature was conceptualised as a Beginning Temporary Teacher Theoretical Framework which served to inform the study. Using a qualitative case study methodology, the research techniques employed for the thesis were semi-structured interview and document analysis. A simultaneously conducted research project in which the researcher participated entitled 'Winning the Lottery? Beginning Teachers on Temporary Engagement' foregrounded this thesis in terms of refining the research question, contributing to the literature and in the selection of the participants. For this case study the perspectives of four distinct yet inter-related categories of professionals were sought. These included four beginning secondary teachers, three school administrators, a Senior Personnel Officer with Education Queensland, and a representative from the Queensland Teachers' Union. The research findings indicated that none of the beginning teachers or other professionals viewed starting a career in teaching on temporary engagement as the ideal. The negative features identified were the differential treatment received and the high level of uncertainty associated with temporary employment. Differential treatment tended to indicate 'less' entitlements, in terms of access to induction and professional development, recreational and sick leave, acceptance by and expectations of other colleagues, and avenues of redress in grievance cases. Moreover, interviews indicated a high level of uncertainty in terms of starting within the teaching profession, commencing at a new school, and a regular income. In addition, frequent changes in schools and/or cohorts of students exacerbated levels of uncertainty. The beginning teachers reported significantly decreased motivation, self-esteem and sense of belonging, and increased stress levels. There was an even more marked negative impact on those beginning teachers who had experienced a higher number of temporary engagements and schools in their first year of teaching. Conversely, strong staff support and a reasonable length of time in the one school improved the quality of the beginning teachers' experiences. The overall impact of being on temporary engagement resulted in delayed permanent position appointments, decreased commitment to particular schools and to Education Queensland as the employing authority, and for two of the beginning teachers, it produced a desire to seek alternative employment. The implementation of Education Queensland's policies relating to working conditions and entitlements for these temporary beginning teachers at the school level was revealed to be less than satisfactory. There was a tendency towards 'just-in- time' management of the beginning teacher on temporary engagement. The beginning teachers received 'less-than-messages' about access to and use of departmental documentation, support through induction and professional development, and their transition from temporary to permanent employment. To ensure a more systematic, supportive and inclusive process for managing the temporary beginning teacher, a conceptual framework entitled 'Continuums of Tension' was developed. The four continuums included permanent employment - temporary employment; system perspective - individual perspective; teaching as a profession - teaching as a job; and the permanent beginning teacher - university graduate. The general principles of the human resource policies of Education Queensland were based on a commitment to permanent employment, a system's perspective, viewing teaching as a profession and a homogeneous group of permanent beginning teachers. Contrasting with this, the beginning teacher on temporary engagement tended to operate from the position of temporary employment and a perspective that was individually based. Their priorities therefore included the 'occupational' aspects of being a temporary teacher striving to become permanent. Thus there existed a tension or contradiction between the general principles of human resource policies within Education Queensland and the employment experiences of beginning teachers on temporary engagement. The study proposed three actions for resolution to address the aforementioned tensions. The actions included: (a) the effective provision and targeted communication of information; (b) support, induction and professional development; and (c) a coordinated approach between Education Queensland, Queensland Teachers' Union, the Universities and the beginning teacher. These actions are fm1her refined to include: (a) an induction kit to suppm1 the individual through the pre-employment to permanent employee phases, (b) an extrapolation of the roles and responsibilities of Education Queensland personnel charged with supporting the beginning temporary teacher, and (c) a series of recommendations to effect a coordinated approach amongst the key stakeholders. The theoretical and conceptual frameworks have provided a means of addressing the identified needs of the beginning teacher on temporary engagement. As such, this study has contributed to the research literature on teacher employment and professionalism and aims to provide a beginning temporary teacher with managed professional and occupational support.

Modelling photochemical production of fine particulates in a toluene/NOx/water vapour system

This work investigates the computer modelling of the photochemical formation of smog products such as ozone and aerosol, in a system containing toluene, NOx and water vapour. In particular, the problem of modelling this process in the Commonwealth Scientific and Industrial Research Organization (CSIRO) smog chambers, which utilize outdoor exposure, is addressed. The primary requirement for such modelling is a knowledge of the photolytic rate coefficients. Photolytic rate coefficients of species other than N02 are often related to JNo2 (rate coefficient for the photolysis ofN02) by a simple factor, but for outdoor chambers, this method is prone to error as the diurnal profiles may not be similar in shape. Three methods for the calculation of diurnal JNo2 are investigated. The most suitable method for incorporation into a general model, is found to be one which determines the photolytic rate coefficients for N02, as well as several other species, from actinic flux, absorption cross section and quantum yields. A computer model was developed, based on this method, to calculate in-chamber photolysis rate coefficients for the CSIRO smog chambers, in which ex-chamber rate coefficients are adjusted by accounting for variation in light intensity by transmittance through the Teflon walls, albedo from the chamber floor and radiation attenuation due to clouds. The photochemical formation of secondary aerosol is investigated in a series of toluene-NOx experiments, which were performed in the CSIRO smog chambers. Three stages of aerosol formation, in plots of total particulate volume versus time, are identified: a delay period in which no significant mass of aerosol is formed, a regime of rapid aerosol formation (regime 1) and a second regime of slowed aerosol formation (regime 2). Two models are presented which were developed from the experimental data. One model is empirically based on observations of discrete stages of aerosol formation and readily allows aerosol growth profiles to be calculated. The second model is based on an adaptation of published toluene photooxidation mechanisms and provides some chemical information about the oxidation products. Both models compare favorably against the experimental data. The gross effects of precursor concentrations (toluene, NOx and H20) and ambient conditions (temperature, photolysis rate) on the formation of secondary aerosol are also investigated, primarily using the mechanism model. An increase in [NOx]o results in increased delay time, rate of aerosol formation in regime 1 and volume of aerosol formed in regime 1. This is due to increased formation of dinitrocresol and furanone products. An increase in toluene results in a decrease in the delay time and an increase in the rate of aerosol formation in regime 1, due to enhanced reactivity from the toluene products, such as the radicals from the photolysis of benzaldehyde. Water vapor has very little effect on the formation of aerosol volume, except that rates are slightly increased due to more OH radicals from reaction with 0(1D) from ozone photolysis. Increased temperature results in increased volume of aerosol formed in regime 1 (increased dinitrocresol formation), while increased photolysis rate results in increased rate of aerosol formation in regime 1. Both the rate and volume of aerosol formed in regime 2 are increased by increased temperature or photolysis rate. Both models indicate that the yield of secondary particulates from hydrocarbons (mass concentration aerosol formed/mass concentration hydrocarbon precursor) is proportional to the ratio [NOx]0/[hydrocarbon]0

Quantifying N2O and CO2 emissions from subtropical pasture

Greenhouse gas emissions from a well established, unfertilized tropical grass-legume pasture were monitored over two consecutive years using high resolution automatic sampling. Nitrous oxide emissions were highest during the summer months and were highly episodic, related more to the size and distribution of rain events than WFPS alone. Mean annual emissions were significantly higher during 2008 (5.7 ± 1.0 g N2O-N/ha/day) than 2007 (3.9 ± 0.4 and g N2O-N/ha/day) despite receiving nearly 500 mm less rain. Mean CO2 (28.2 ± 1.5 kg CO2 C/ha/day) was not significantly different (P < 0.01) between measurement years, emissions being highly dependent on temperature. A negative correlation between CO2 and WFPS at >70% indicated a threshold for soil conditions favouring denitrification. The use of automatic chambers for high resolution greenhouse gas sampling can greatly reduce emission estimation errors associated with temperature and WFPS changes.

Pastureland use in the southeastern US: Implications for carbon sequestration

More than 13 Mha of nonfederal land in the southeastern U.S. are devoted to pastureland. Between 1982 and 1992, pastureland increased by 100,000 ha, with nearly 70% converted from cultivated land. We examined the potential for carbon (C) sequestration with improved pasture management and conversion into pastureland from cultivated land. Improved pasture management techniques, such as intensive grazing, fertilization, introduction of improved grass and legume species, and better irrigation systems can lead to sequestration of atmospheric C in soil. Literature values for the influence of changes in pasture management on soil C were summarized for several potential management changes in the Southeast. Soil C sequestration estimates for the Southeast were based on current pasture management practices and evaluated for a range of different adoption rates of improved practices. Conversion into pasture can also potentially sequester significant amounts of atmospheric C in soils. Land-use data from the National Resources Inventory and literature estimates of soil C changes following conversion to pasture were used to estimate historical (1982 to 1992) soil C sequestration in pastures. Potential future sequestration was estimated based on extrapolation of land-use trends between 1982 and 1992. With continued conversion into pasture and improvement of pasture management, southeastern U.S. pasture soils may be a significant C sink for several years.

Diagnostic and treatment pathways for men with prostate cancer in Queensland : investigating spatial and demographic inequalities

Background: Patterns of diagnosis and management for men diagnosed with prostate cancer in Queensland, Australia, have not yet been systematically documented and so assumptions of equity are untested. This longitudinal study investigates the association between prostate cancer diagnostic and treatment outcomes and key area-level characteristics and individual-level demographic, clinical and psychosocial factors.---------- Methods/Design: A total of 1064 men diagnosed with prostate cancer between February 2005 and July 2007 were recruited through hospital-based urology outpatient clinics and private practices in the centres of Brisbane, Townsville and Mackay (82% of those referred). Additional clinical and diagnostic information for all 6609 men diagnosed with prostate cancer in Queensland during the study period was obtained via the population-based Queensland Cancer Registry. Respondent data are collected using telephone and self-administered questionnaires at pre-treatment and at 2 months, 6 months, 12 months, 24 months, 36 months, 48 months and 60 months post-treatment. Assessments include demographics, medical history, patterns of care, disease and treatment characteristics together with outcomes associated with prostate cancer, as well as information about quality of life and psychological adjustment. Complementary detailed treatment information is abstracted from participants’ medical records held in hospitals and private treatment facilities and collated with health service utilisation data obtained from Medicare Australia. Information about the characteristics of geographical areas is being obtained from data custodians such as the Australian Bureau of Statistics. Geo-coding and spatial technology will be used to calculate road travel distances from patients’ residences to treatment centres. Analyses will be conducted using standard statistical methods along with multilevel regression models including individual and area-level components.---------- Conclusions: Information about the diagnostic and treatment patterns of men diagnosed with prostate cancer is crucial for rational planning and development of health delivery and supportive care services to ensure equitable access to health services, regardless of geographical location and individual characteristics. This study is a secondary outcome of the randomised controlled trial registered with the Australian New Zealand Clinical Trials Registry (ACTRN12607000233426)

Remaining useful life prediction using elliptical basis function network and Markov Chain

This paper presents a novel method for remaining useful life prediction using the Elliptical Basis Function (EBF) network and a Markov chain. The EBF structure is trained by a modified Expectation-Maximization (EM) algorithm in order to take into account the missing covariate set. No explicit extrapolation is needed for internal covariates while a Markov chain is constructed to represent the evolution of external covariates in the study. The estimated external and the unknown internal covariates constitute an incomplete covariate set which are then used and analyzed by the EBF network to provide survival information of the asset. It is shown in the case study that the method slightly underestimates the remaining useful life of an asset which is a desirable result for early maintenance decision and resource planning.

Making sense of brain tumour: A qualitative investigation of personal and social processes of adjustment

This study investigated personal and social processes of adjustment at different stages of illness for individuals with brain tumour. A purposive sample of 18 participants with mixed tumour types (9 benign and 9 malignant) and 15 family caregivers was recruited from a neurosurgical practice and a brain tumour support service. In-depth semi-structured interviews focused on participants’ perceptions of their adjustment, including personal appraisals, coping and social support since their brain tumour diagnosis. Interview transcripts were analysed thematically using open, axial and selective coding techniques. The primary theme that emerged from the analysis entailed “key sense making appraisals”, which was closely related to the following secondary themes: (1) Interactions with those in the healthcare system, (2) reactions and support from the personal support network, and (3) a diversity of coping efforts. Adjustment to brain tumour involved a series of appraisals about the illness that were influenced by interactions with those in the healthcare system, reactions and support from people in their support network, and personal coping efforts. Overall, the findings indicate that adjustment to brain tumour is highly individualistic; however, some common personal and social processes are evident in how people make sense of and adapt to the illness over time. A preliminary framework of adjustment based on the present findings and its clinical relevance are discussed. In particular, it is important for health professionals to seek to understand and support individuals’ sense-making processes following diagnosis of brain tumour.