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 first Australian nurse practitioner census : a protocol to guide standardized collection of information about an emergent professional group

Internationally, collection of reliable data on new and evolving health-care roles is crucial. We describe a protocol for design and administration of a national census of an emergent health-care role, namely nurse practitioners in Australia using databases held by regulatory authorities. A questionnaire was developed to obtain data on the role and scope of practice of Australian nurse practitioners. Our tool comprised five sections and included a total of 56 questions, using 28 existing items from the National Nursing and Midwifery Labour Force Census and nine items recommended in the Nurse Practitioner Workforce Planning Minimum Data Set. Australian Nurse Registering Authorities (n = 6) distributed the survey on our behalf. This paper outlines our instrument and methods. The survey was administered to 238 authorized Australian nurse practitioners (85% response rate). Rigorous collection of standardized items will ensure health policy is informed by reliable and valid data. We will re-administer the survey 2 years following the first survey to measure change over time.

Trends in Australian contact lens prescribing during the first decade of the 21st Century (2000–2009)

Purpose: The aim was to document contact lens prescribing trends in Australia between 2000 and 2009. ---------- Methods: A survey of contact lens prescribing trends was conducted each year between 2000 and 2009. Australian optometrists were asked to provide information relating to 10 consecutive contact lens fittings between January and March each year. ---------- Results: Over the 10-year survey period, 1,462 practitioners returned survey forms representing a total of 13,721 contact lens fittings. The mean age (± SD) of lens wearers was 33.2 ± 13.6 years and 65 per cent were female. Between 2006 and 2009, rigid lens new fittings decreased from 18 to one per cent. Low water content lenses reduced from 11.5 to 3.2 per cent of soft lens fittings between 2000 and 2008. Between 2005 and 2009, toric lenses and multifocal lenses represented 26 and eight per cent, respectively, of all soft lenses fitted. Daily disposable, one- to two-week replacement and monthly replacement lenses accounted for 11.6, 30.0 and 46.5 per cent of all soft lens fittings over the survey period, respectively. The proportion of new soft fittings and refittings prescribed as extended wear has generally declined throughout the past decade. Multi-purpose lens care solutions dominate the market. Rigid lenses and monthly replacement soft lenses are predominantly worn on a full-time basis, whereas daily disposable soft lenses are mainly worn part-time.---------- Conclusions: This survey indicates that technological advances, such as the development of new lens materials, manufacturing methods and lens designs, and the availability of various lens replacement options, have had a significant impact on the contact lens market during the first decade of the 21st Century.

Twenty first century trends in silicone hydrogel contact lens fitting : an international perspective

Silicone hydrogel contact lenses were introduced into the market in 1999. To assess prescribing trends of this lens type since then, up to 1000 survey forms were sent to contact lens fitters in Australia, Canada, Japan, the Netherlands, Norway, the UK and the USA each year between 2000 and 2008. Practitioners were asked to record data relating to the first 10 contact lens fits or refits performed after receiving the survey form. Analysis of returned forms revealed a rapid increase in the prescribing of silicone hydrogel lenses over the survey period. In 2008, silicone hydrogel lenses represented 36% of all soft lenses prescribed. The categorization of the majority of lenses prescribed as ‘refits’ is primarily attributed to the mass conversion of lens wearers from hydrogel to silicone hydrogel lenses. Silicone hydrogels may soon represent the majority of soft contact lenses prescribed.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

How I became the first Aboriginal person in Australia to lead a national education organisation

In this paper, Bronwyn Fredericks reflects on how, in 1997, she became the National President of the Council of Australian Postgraduate Associations Inc. (CAPA). The paper describes the election process faced by Fredericks, and identifies some of her key achievements during her time as National President. In becoming the National President, Bronwyn became the first Aboriginal person in Australia to lead a national education organisation. The story within this paper is told from the author’s autobiographical memory, drawing on the cultural, social and political context in which the story and the author were (and are) situated (Wojecki 2007). In this way the story teller reveals story lines which have not previously been articulated (Wojecki 2007). Throughout this paper, Fredericks ‘re-stories’ her experiences of leadership.

The relationship between Australians and the overseas graves of the First World War

The purpose of this thesis is to outline the relationship that existed in the past and exists in the present, between Australians and the War Graves and Memorials to the Missing. commemorations of Australians who died during the First World War. Their final resting places are scattered all over the world and provide a tangible record of the sacrifice of men and women in the war, and represent the final result by Official Agencies such as the Imperial, and later, Commonwealth War Graves Commission, and its agency representative, the Office of Australian War Graves, of an attempt to appropriately commemorate them. The study follows the path of history from the event of death of an individual in the First World War, through their burial; temporary grave or memorial commemoration; the permanent commemoration; the family and public reaction to the deaths; how the Official Agencies of related Commonwealth Governments dealt with the dead; and finally, how the Australian dead are represented on the battlefields of the world in the 21st century. Australia.s war dead of the First World War are scattered around the globe in more than 40 countries and are represented in war cemeteries and civil cemeteries; and listed on large „Memorials to the Missing., which commemorate the individuals devoid of a known graves or final resting place.

The first global entertainment company : explaining Pathe's dominance in the pre-Hollywood film industry

For almost a decade before Hollywood existed, French firm Pathe towered over the early film industry with estimates of its share of all films sold around the world varying between 50-70%. Pathe was the first global entertainment company. This paper analyses its rise to market leadership by applying a theoretical framework drawn from the business literature on causes of industry dominance, which provides insights into how firms acquire and maintain market dominance and in this case the film industry. This paper uses evidence presented by film historians to argue that Pathe "fits" the expected theoretical model of a dominant firm because it had a marketing orientation, used an effective quality-based competitive strategy and possessed the six critical marketing capabilities that business research shows enable the best performing firms to consistently outperform rivals.

Peer-to-Patent Australia: First Anniversary Report, December 2010

Peer-to-Patent Australia will initially run as a 12 month pilot project designed to test whether an open community of reviewers can effectively locate prior art that might not otherwise be located by the patent office during a typical examination. Patent applications will be made available for peer review for a period of 6 months and there will follow a 6 month period of joint qualitative and quantitative assessment of the pilot project by IP Australia and QUT. The objective of Peer-to-Patent Australia is to improve the patent examination process and the quality of issued patents by utilising the knowledge and skills of experts in the broader community. It is a way of linking the scientific and technical expertise of anyone with an Internet connection with the expertise of a patent examiner. That community participation consists of members of the public reviewing patent applications and contributing relevant prior art references and comments within a web-based forum. The aim is to bring to light prior art, particularly non-patent prior art, that might otherwise not be identified by patent examiners. The better the prior art resources a patent examiner has at his or her disposal, the more likely a patent application will be assessed properly in terms of novelty and inventive step. The role of Peer-to-Patent Australia in this regard is to act as both a facilitator of discussion and a collector of prior art submissions. Peer-to-Patent Australia collects relevant prior art references on behalf of the reviewing community and forwards that prior art to IP Australia. Section 27 of the Patents Act 1990 (Cth) allows for the Commissioner of Patents to receive submissions of prior art by third parties relevant to the novelty and inventiveness of a particular patent application.

Creative industries after the first decade of debate

It has now been over a decade since the concept of creative industries was first put into the public domain through the Creative Industries Mapping Documents developed by the Blair Labour government in Britain. The concept has developed traction globally, but it has also been understood and developed in different ways in Europe, Asia, Australia, New Zealand and North America, as well as through international bodies such as UNCTAD and UNESCO. A review of the policy literature reveals that while questions and issues remain around definitional coherence, there is some degree of consensus emerging about the size, scope and significance of the sectors in question in both advanced and developing economies. At the same time, debate about the concept remains highly animated in media, communication and cultural studies, with its critics dismissing the concept outright as a harbinger of neo-liberal ideology in the cultural sphere. This paper couches such critiques in light of recent debates surrounding the intellectual coherence of the concept of neo-liberalism, arguing that this term itself possesses problems when taken outside of the Anglo-American context in which it originated. It is argued that issues surrounding the nature of participatory media culture, the relationship between cultural production and economic innovation, and the future role of public cultural institutions can be developed from within a creative industries framework, and that writing off such arguments as a priori ideological and flawed does little to advance debates about 21st century information and media culture.

Delivering value for money in the procurement of public sector major infrastructure : a new first-order decision making model

The significant challenge faced by government in demonstrating value for money in the delivery of major infrastructure resolves around estimating costs and benefits of alternative modes of procurement. Faced with this challenge, one approach is to focus on a dominant performance outcome visible on the opening day of the asset, as the means to select the procurement approach. In this case, value for money becomes a largely nominal concept and determined by selected procurement mode delivering, or not delivering, the selected performance outcome, and notwithstanding possible under delivery on other desirable performance outcomes, as well as possibly incurring excessive transaction costs. This paper proposes a mind-set change in this particular practice, to an approach in which the analysis commences with the conditions pertaining to the project and proceeds to deploy transaction cost and production cost theory to indicate a procurement approach that can claim superior value for money relative to other competing procurement modes. This approach to delivering value for money in relative terms is developed in a first-order procurement decision making model outlined in this paper. The model developed could be complementary to the Public Sector Comparator (PSC) in terms of cross validation and the model more readily lends itself to public dissemination. As a possible alternative to the PSC, the model could save time and money in preparation of project details to lesser extent than that required in the reference project and may send a stronger signal to the market that may encourage more innovation and competition.