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.

The design and testing of a daylighting device : optimising the energy and optical performance of Australian commercial buildings

The effective daylighting of multistorey commercial building interiors poses an interesting problem for designers in Australia’s tropical and subtropical context. Given that a building exterior receives adequate sun and skylight as dictated by location-specific factors such as weather, siting and external obstructions; then the availability of daylight throughout its interior is dependant on certain building characteristics: the distance from a window façade (room depth), ceiling or window head height, window size and the visible transmittance of daylighting apertures. The daylighting of general stock, multistorey commercial buildings is made difficult by their design limitations with respect to some of these characteristics. The admission of daylight to these interiors is usually exclusively by vertical windows. Using conventional glazing, such windows can only admit sun and skylight to a depth of approximately 2 times the window height. This penetration depth is typically much less than the depth of the office interiors, so that core areas of these buildings receive little or no daylight. This issue is particularly relevant where deep, open plan office layouts prevail. The resulting interior daylight pattern is a relatively narrow perimeter zone bathed in (sometimes too intense) light, contrasted with a poorly daylit core zone. The broad luminance range this may present to a building occupant’s visual field can be a source of discomfort glare. Furthermore, the need in most tropical and subtropical regions to restrict solar heat gains to building interiors for much of the year has resulted in the widespread use of heavily tinted or reflective glazing on commercial building façades. This strategy reduces the amount of solar radiation admitted to the interior, thereby decreasing daylight levels proportionately throughout. However this technique does little to improve the way light is distributed throughout the office space. Where clear skies dominate weather conditions, at different times of day or year direct sunlight may pass unobstructed through vertical windows causing disability or discomfort glare for building occupants and as such, its admission to an interior must be appropriately controlled. Any daylighting system to be applied to multistorey commercial buildings must consider these design obstacles, and attempt to improve the distribution of daylight throughout these deep, sidelit office spaces without causing glare conditions. The research described in this thesis delineates first the design optimisation and then the actual prototyping and manufacture process of a daylighting device to be applied to such multistorey buildings in tropical and subtropical environments.

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Productions of space : civic participation of young people at university

Civic participation of young people around the world is routinely described in deficit terms, as they are labelled apathetic, devoid of political knowledge, disengaged from the community and self-absorbed (Andolina, 2002; Weller, 2006). This paper argues that the connectivity of time, space and social values (Lefebvre, 1991; Soja, 1996) are integral to understanding the performances of young people as civic subjects. Today’s youth negotiate unstable social, economic and environmental conditions, new technologies and new forms of community. Loyalty, citizenship and notions of belonging take on new meanings in these changing global conditions. Using the socio-spatial theories of Lefebvre and Foucault, and the tools of critical discourse analysis, this paper argues that the chronotope, or time/space relationship of universities, produces student citizens who, in resistance to a complex global society, create a cocooned space which focuses on moral and spiritual values that can be enacted on a personal level.

Best practices in prediction for decision-making : lessons from the atmospheric and earth sciences

Predictions that result from scientific research hold great appeal for decision-makers who are grappling with complex and controversial environmental issues, by promising to enhance their ability to determine a need for and outcomes of alternative decisions. A problem exists in that decision-makers and scientists in the public and private sectors solicit, produce, and use such predictions with little understanding of their accuracy or utility, and often without systematic evaluation or mechanisms of accountability. In order to contribute to a more effective role for ecological science in support of decision-making, this paper discusses three ``best practices'' for quantitative ecosystem modeling and prediction gleaned from research on modeling, prediction, and decision-making in the atmospheric and earth sciences. The lessons are distilled from a series of case studies and placed into the specific context of examples from ecological science.

The Space Day at QUT

The Space Day has been running at QUT for about a decade. The Space Day started out as a single lecture on the stars delivered to a group of high school students from Brisbane State High School (BSHS), just across the river from QUT and therefore convenient for the school to visit. I was contacted by Victor James of St. Laurence’s College (SLC), Brisbane asking if he could bring a group of boys to QUT for a lecture similar to that delivered to BSHS. However, for SLC a hands-on laboratory session was added to the lecture and thus the Space Day was born. For the Space Day we have concentrated on year 7 – 10 students. Subsequently, many other schools from Brisbane and further afield in Queensland have attended a Space Day.

Lift@Weimar : sustainable interaction with food, technology, and the city (Workshop)

This workshop explores innovative approaches to understanding and cultivating sustainable food culture in urban environments via human-computer-interaction (HCI) design and ubiquitous technologies. We perceive the city as an intersecting network of people, place, and technology in constant transformation. Our 2009 OZCHI workshop, Hungry 24/7? HCI Design for Sustainable Food Culture, opened a new space for discussion on this intersection amongst researchers and practitioners from diverse backgrounds including academia, government, industry, and non-for-profit organisations. Building on the past success, this new instalment of the workshop series takes a more refined view on mobile human-food interaction and the role of interactive media in engaging citizens to cultivate more sustainable everyday human-food interactions on the go. Interactive media in this sense is distributed, pervasive, and embedded in the city as a network. The workshop addresses environmental, health, and social domains of sustainability by bringing together insights across disciplines to discuss conceptual and design approaches in orchestrating mobility and interaction of people and food in the city as a network of people, place, technology, and food.

Pandemic (H1N1) 2009 Influenza Outbreak in Australia: Impact on Emergency Departments.

Executive summary Objective: The aims of this study were to identify the impact of Pandemic (H1N1) 2009 Influenza on Australian Emergency Departments (EDs) and their staff, and to inform planning, preparedness, and response management arrangements for future pandemics, as well as managing infectious patients presenting to EDs in everyday practice. Methods This study involved three elements: 1. The first element of the study was an examination of published material including published statistics. Standard literature research methods were used to identify relevant published articles. In addition, data about ED demand was obtained from Australian Government Department of Health and Ageing (DoHA) publications, with several state health departments providing more detailed data. 2. The second element of the study was a survey of Directors of Emergency Medicine identified with the assistance of the Australasian College for Emergency Medicine (ACEM). This survey retrieved data about demand for ED services and elicited qualitative comments on the impact of the pandemic on ED management. 3. The third element of the study was a survey of ED staff. A questionnaire was emailed to members of three professional colleges—the ACEM; the Australian College of Emergency Nursing (ACEN); and the College of Emergency Nursing Australasia (CENA). The overall response rate for the survey was 18.4%, with 618 usable responses from 3355 distributed questionnaires. Topics covered by the survey included ED conditions during the (H1N1) 2009 influenza pandemic; information received about Pandemic (H1N1) 2009 Influenza; pandemic plans; the impact of the pandemic on ED staff with respect to stress; illness prevention measures; support received from others in work role; staff and others’ illness during the pandemic; other factors causing ED staff to miss work during the pandemic; and vaccination against Pandemic (H1N1) 2009 Influenza. Both qualitative and quantitative data were collected and analysed. Results: The results obtained from Directors of Emergency Medicine quantifying the impact of the pandemic were too limited for interpretation. Data sourced from health departments and published sources demonstrated an increase in influenza-like illness (ILI) presentations of between one and a half and three times the normal level of presentations of ILIs. Directors of Emergency Medicine reported a reasonable level of preparation for the pandemic, with most reporting the use of pandemic plans that translated into relatively effective operational infection control responses. Directors reported a highly significant impact on EDs and their staff from the pandemic. Growth in demand and related ED congestion were highly significant factors causing distress within the departments. Most (64%) respondents established a ‘flu clinic’ either as part of Pandemic (H1N1) 2009 Influenza Outbreak in Australia: Impact on Emergency Departments. the ED operations or external to it. They did not note a significantly higher rate of sick leave than usual. Responses relating to the impact on staff were proportional to the size of the colleges. Most respondents felt strongly that Pandemic (H1N1) 2009 Influenza had a significant impact on demand in their ED, with most patients having low levels of clinical urgency. Most respondents felt that the pandemic had a negative impact on the care of other patients, and 94% revealed some increase in stress due to lack of space for patients, increased demand, and filling staff deficits. Levels of concern about themselves or their family members contracting the illness were less significant than expected. Nurses displayed significantly higher levels of stress overall, particularly in relation to skill-mix requirements, lack of supplies and equipment, and patient and patients’ family aggression. More than one-third of respondents became ill with an ILI. Whilst respondents themselves reported taking low levels of sick leave, respondents cited difficulties with replacing absent staff. Ranked from highest to lowest, respondents gained useful support from ED colleagues, ED administration, their hospital occupational health department, hospital administration, professional colleges, state health department, and their unions. Respondents were generally positive about the information they received overall; however, the volume of information was considered excessive and sometimes inconsistent. The media was criticised as scaremongering and sensationalist and as being the cause of many unnecessary presentations to EDs. Of concern to the investigators was that a large proportion (43%) of respondents did not know whether a pandemic plan existed for their department or hospital. A small number of staff reported being redeployed from their usual workplace for personal risk factors or operational reasons. As at the time of survey (29 October –18 December 2009), 26% of ED staff reported being vaccinated against Pandemic (H1N1) 2009 Influenza. Of those not vaccinated, half indicated they would ‘definitely’ or ‘probably’ not get vaccinated, with the main reasons being the vaccine was ‘rushed into production’, ‘not properly tested’, ‘came out too late’, or not needed due to prior infection or exposure, or due to the mildness of the disease. Conclusion: Pandemic (H1N1) 2009 Influenza had a significant impact on Australian Emergency Departments. The pandemic exposed problems in existing plans, particularly a lack of guidelines, general information overload, and confusion due to the lack of a single authoritative information source. Of concern was the high proportion of respondents who did not know if their hospital or department had a pandemic plan. Nationally, the pandemic communication strategy needs a detailed review, with more engagement with media networks to encourage responsible and consistent reporting. Also of concern was the low level of immunisation, and the low level of intention to accept vaccination. This is a problem seen in many previous studies relating to seasonal influenza and health care workers. The design of EDs needs to be addressed to better manage infectious patients. Significant workforce issues were confronted in this pandemic, including maintaining appropriate staffing levels; staff exposure to illness; access to, and appropriate use of, personal protective equipment (PPE); and the difficulties associated with working in PPE for prolonged periods. An administrative issue of note was the reporting requirement, which created considerable additional stress for staff within EDs. Peer and local support strategies helped ensure staff felt their needs were provided for, creating resilience, dependability, and stability in the ED workforce. Policies regarding the establishment of flu clinics need to be reviewed. The ability to create surge capacity within EDs by considering staffing, equipment, physical space, and stores is of primary importance for future pandemics.