A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Cause of Death, Trend and Disease Burden in Shandong Province, China : the Third Retrospective Sampling Survey of Cause of Death Report

This book describes the mortality for all causes of death and the trend in major causes of death since 1970s in Shandong Province, China.

Creative intersections : supervision, practice and the space between

Supervision in the creative arts is a topic of growing significance since the increase in creative practice PhDs across universities in Australasia. This presentation will provide context of existing discussions in creative practice and supervision. Creative practice – encompassing practice-based or practice-led research – has now a rich history of research surrounding it. Although it is a comparatively new area of knowledge, great advances have been made in terms of how practice can influence, generate, and become research. The practice of supervision is also a topic of interest, perhaps unsurprisingly considering its necessity within the university environment. Many scholars have written much about supervision practices and the importance of the supervisory role, both in academic and more informal forms. However, there is an obvious space in between: there is very little research on supervision practices within creative practice higher degrees, especially at PhD or doctorate level. Despite the existence of creative practice PhD programs, and thus the inherent necessity for successful supervisors, there remain minimal publications and limited resources available. Creative Intersections explores the existing publications and resources, and illustrates that a space for new published knowledge and tools exists.

Legal Profession Act 2007 : entitlement to itemised bill – meaning of “client” – meaning of “third party payer”

In Legal Services Commissioner and Wright [2010] QSC 168 and Amos v Ian K Fry & Company, the Supreme Court of Queensland considered the scope of some of the provisions of the Legal Profession Act 2007 (Qld), including the definition of “third party payer” in s 301 of the Act.

Legal Profession Act 2004 (NSW) : costs agreement between law practice and client - whether binding on non-associated third party payer

The decision in the New South Wales Supreme Court in Boyce v McIntyre [2008] NSWSC 1218 involved determination of a number of issues relating to an assessment of costs under the Legal Profession Act 2004 (NSW). The issue of broad significance was whether a non-associated third party payer must pay the fixed fee that was agreed between the law practice and the client. The court found that the client agreement did not form the basis of assessing costs for the non-associated third party payer.

Making Arrangements : Remote proposal sequences and attendant structural phenomena in social interaction

In this thesis, I contribute to the study of how arrangements are made in social interaction. Using conversation analysis, I examine a corpus of 375 telephone calls between employees and clients of three Community Home Care (CHC) service agencies in metropolitan Adelaide, South Australia. My analysis of the CHC data corpus draws upon existing empirical findings within conversation analysis in order to generate novel findings about how people make arrangements with one another, and some of the attendant considerations that parties to such an activity can engage in: Prospective informings as remote proposals for a future arrangement – Focusing on how employees make arrangements with clients, I show how the employees in the CHC data corpus use ‘prospective informings’ to detail a future course of action that will involve the recipient of that informing. These informings routinely occasion a double-paired sequence, where informers pursue a response to their informing. This pursuit often occurs even after recipients have provided an initial response. This practice for making arrangements has been previously described by Houtkoop (1987) as ‘remote proposing.’ I develop Houtkoop’s analysis to show how an informing of a future arrangement can be recompleted, with response solicitation, as a proposal that is contingent upon a recipient’s acceptance. Participants’ understanding of references to non-present third parties – In the process of making arrangements, references are routinely made to non-present third parties. In the CHC data corpus, these third parties are usually care workers. Prior research (e.g., Sacks & Schegloff, 1979; Schegloff, 1996b) explains how the use of ‘recognitional references’ (such as the bare name ‘Kerry’), conveys to recipients that they should be able to locate the referent from amongst their acquaintances. Conversely, the use of ‘non-recognitional references’ (such as the description ‘a lady called Kerry’), conveys that recipients are unacquainted with the referent. I examine instances where the selection of a recognitional or non-recognitional reference form is followed by a recipient initiating repair on that reference. My analysis provides further evidence thatthe existing analytic account of these references corresponds to the way in which participants themselves make sense of them. My analysis also advances an understanding of how repair can be used, by recipients, to indicate the inappositeness of a prior turn. Post-possible-completion accounts – In a case study of a problematic interaction, I examine a misunderstanding that is not resolved within the repair space, the usual defence of intersubjectivity in interaction (cf. Schegloff, 1992b). Rather, I explore how the source of trouble is addressed, outside of the sequence of its production, with a ‘post-possible-completion account.’ This account specifies the basis of a misunderstanding and yet, unlike repair, does so without occasioning a revised response to a trouble-source turn. By considering various aspects of making arrangements in social interaction, I highlight some of the rich order that underpins the maintenance of human relationships across time. In the concluding section of this thesis I review this order, while also discussing practical implications of this analysis for CHC practice.

A sustainable tourism development in Alacati, Turkey : (Re)invention of public space with clean energy

Although there is an increasing recognition of the impacts of climate change on communities, residents often resist changing their lifestyle to reduce the effects of the problem. By using a landscape architectural design medium, this paper argues that public space, when designed as an ecological system, has the capacity to create social and environmental change and to increase the quality of the human environment. At the same time, this ecological system can engage residents, enrich the local economy, and increase the social network. Through methods of design, research and case study analysis, an alternative master plan is proposed for a sustainable tourism development in Alacati, Turkey. Our master plan uses local geographical, economic and social information within a sustainable landscape architectural design scheme that addresses the key issues of ecology, employment, public space and community cohesion. A preliminary community empowerment model (CEM) is proposed to manage the designs. The designs address: the coexistence of local agricultural and sustainable energy generation; state of the art water management; and the functional and sustainable social and economic interrelationship of inhabitants, NGOs, and local government.

Stratospheric dust collections : valuable resources for space and atmospheric scientists

Collections of solid particles from the Earths' stratosphere have been a significant part of atmospheric research programs since 1965 [1], but it has only been in the past decade that space-related disciplines have provided the impetus for a continued interest in these collections. Early research on specific particle types collected from the stratosphere established that interplanetary dust particles (IDP's) can be collected efficiently and in reasonable abundance using flat-plate collectors [2-4]. The tenacity of Brownlee and co-workers in this subfield of cosmochemistry has led to the establishment of a successful IDP collection and analysis program (using flat-plate collectors on high-flying aircraft) based on samples available for distribution from Johnson Space Center [5]. Other stratospheric collections are made, but the program at JSC offers a unique opportunity to study well-documented, individual particles (or groups of particles) from a wide variety of sources [6]. The nature of the collection and curation process, as well as the timeliness of some sampling periods [7], ensures that all data obtained from stratospheric particles is a valuable resource for scientists from a wide range of disciplines. A few examples of the uses of these stratospheric dust collections are outlined below.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

Influencing the experience of people in urban public places through mobile mediated interactions

This study presents research findings to informthe design and development of innovativemobile services aiming to enable collocated people to interact with each other in public urban places. The main goal of this research is to provide applications and deliver guidelines to positively influence the user experience of different public urban places during everyday urban life. This study describes the design and evaluation of mobile content and services enabling mobile mediated interactions in an anonymous way. The research described in this thesis is threefold. First, this study investigates how Information and Communication Technology (ICT) can be utilised in particular urban public places to influence the experience of urban dwellers during everyday life. The research into urban residents and public places guides the design of three different technologies that form case studies to investigate and discover possibilities to digitally augment the public urban space and make the invisible data of our interactions in the urban environment visible. • Capital Music enables urban dwellers to listen to their music on their mobile devices as usual but also visualises the artworks of songs currently being played and listened to by other users in ones’ vicinity. • PlaceTagz uses QR codes printed on stickers that link to a digital message board enabling collocated users to interact with each other over time resulting in a place-based digital memory. • Sapporo World Window, Brisbane Hot Spots, and YourScreen are interactive content applications allowing people to share data with their mobile phones on public urban screens. The applications employ mobile phones to mediate interactions in form of location and video sharing. Second, this study sets out to explore the quality and nature of the experiences created through the developed and deployed case study applications. The development of a user experience framework for evaluating mobile mediated interactions in urban public places is described and applied within each case. Third, drawing on research from urban sociology, psychology, urban design, and the findings from this study, this thesis discusses how such interactions can have an impact on the urban experience.

Elegy To space

Poem

The study of design elements and people’s behaviour in campus public space : how design shapes user’s behaviour

A growing body of researches provided evidence of the successful design in particular focus on design elements, ranging from colour, lighting, technology, landscape and spatial arrangement. However, no example or literature investigates the opportunities for linking these design elements in a practical base. Drawing upon existing architectural design theory, this paper investigates the relationship between design elements regards to public’s behavioural response to the public space. The aims of this paper are two-fold: first to examine whether there is a direct relationship between the two, and second to find out how the design elements could be coordinated together to influence not only the activities but also the environment, function and experience. To meet this objective, observation, behavioural mapping, interview and cognitive mapping methodologies are used. The present study involves two local case studies to find out the relationship between design elements in order to assist the design of a better public space for public activities. Correlation between the design elements shows that public activities is more likely to happen in relatively space with well balance of design. These finding provide a better understanding of public space design by gaining deeper perceptive between design and user’s behaviour, consequently improving social activities and interactions in public space. Moreover, it focuses on campus public areas which can be a vital aspect of university campus and play a valuable role in the overall success of public space design.