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.

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.

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.

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.

Rejuvenating lost and disused space within Fortitude Valley : a study into the effectiveness of urban greenery in subtropical public space

An issue gaining prominence in our urban environments in the notion of lost space, the undesirable urban areas that are in need of redesign, commonly caused by a focus on development as individual architectural entities, without a greater view of the urban environment as a holistic entity. Within the context of South East Queensland, the suburb of Fortitude Valley has been earmarked for development as an extension of the current CBD. With lost and disused spaces already existing throughout the suburb due to rapid growth and mismatched developments, recent planning regimes have proposed rejuvenation in the form of proposals that echo typologies from other Australian regions, such as the laneway typology from Melbourne. Opportunities exist in these spaces for design approaches that relate specifically to the individual and unique subtropical character of the area. This research explores the relationship between innovative approaches towards urban greenery as a means to rejuvenate lost and disused public space, and its suitability within a subtropical climate, specifically focused within the suburb of Fortitude Valley. A trend gaining prominence is the notion of biophilic cities; cities that integrate urban greenery as a means to provide vibrant public spaces, and meet the growing aesthetic, social, cultural and economic needs of our cities. Through analysis of case studies showcasing greenery in an inventive way, observations of public using subtropical public space, and a discussion of the current policy frameworks at place within Fortitude Valley, innovative uses of urban greenery is proposed as viable placemaking technique in subtropical urban environments.

Applying maintenance strategies from the space and satellite sector to the upstream oil and gas industry : a research agenda

Practitioners from both the upstream oil and gas industry and the space and satellite sector have repeatedly noted several striking similarities between the two industries over the years, which have in turn resulted in many direct comparisons in the media and industry press. The two sectors have previously worked together and shared ideas in ways that have yielded some important breakthroughs, but relatively little sharing or cross-pollination has occurred in the area of asset maintenance. This is somewhat surprising in light of the fact that here, too, the sectors have much in common. This paper accordingly puts forward the viewpoint that the upstream oil and gas industry could potentially make significant improvements in asset maintenance—specifically, with regard to offshore platforms and remote pipelines—by selectively applying some aspects of the maintenance strategies and philosophies that have been learned in the space and satellite sector. The paper then offers a research agenda toward accelerating the rate of learning and sharing between the two industries in this domain, and concludes with policy recommendations that could facilitate this kind of cross-industry learning.

Making space and place for knowledge communities : lessons for Australian practice

This paper aims to shed light on the planning and development processes of the knowledge-based urban development phenomenon, with respect to the construction of knowledge community precincts. We undertake policy and best practice analyses to learn from the planning and development processes of internationally renowned knowledge community precincts—from Copenhagen, Eindhoven and Singapore. In the light of this, we scrutinise major Australian knowledge community precinct initiatives—from Sydney, Melbourne and Brisbane—to better understand the dynamics of national practices, and benchmark them against the international best practice cases. The paper concludes with a discussion on the study findings and successfully establishing space and place for both knowledge economy and society in Australian cities.

Humans, ‘things’ and space : costing hospital infection control interventions

Background: Previous attempts at costing infection control programmes have tended to focus on accounting costs rather than economic costs. For studies using economic costs, estimates tend to be quite crude and probably underestimate the true cost. One of the largest costs of any intervention is staff time, but this cost is difficult to quantify and has been largely ignored in previous attempts. Aim: To design and evaluate the costs of hospital-based infection control interventions or programmes. This article also discusses several issues to consider when costing interventions, and suggests strategies for overcoming these issues. Methods: Previous literature and techniques in both health economics and psychology are reviewed and synthesized. Findings: This article provides a set of generic, transferable costing guidelines. Key principles such as definition of study scope and focus on large costs, as well as pitfalls (e.g. overconfidence and uncertainty), are discussed. Conclusion: These new guidelines can be used by hospital staff and other researchers to cost their infection control programmes and interventions more accurately.

Socio-Spatial Approaches To Literacy Studies: Rethinking the Social Constitution and Politics of Space

Literacy studies have begun to examine the spatial dimension of literacy practices in a way that foregrounds space, and that considers space as constitutive to human relations and practices. This chapter provides an introduction to spatial literacy research, providing a guide to key theorists, themes, and studies that have shaped historical and new developments in spatial approaches to literacy practice and pedagogy. It begins by reconceptualising socio-spatial approaches to literacy research and defines terms. Intersections with related social theories are examined, with an emphasis on critical approaches and the politics of space. It clarifies the relationship between socio-spatial and socio-cultural paradigms, revisiting the spatial in seminal socio-cultural research. It covers new ground,including networks, flows, and deterritorialisation of literacy practice. The chapter concludes with challenges and recommendations for future language research and educational practice.