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.

Structural characterisation and environmental application of organoclays for the removal of phenolic compounds

Modified montmorillonite was prepared at different surfactant (HDTMA) loadings through ion exchange. The conformational arrangement of the loaded surfactants within the interlayer space of MMT was obtained by computational modelling. The conformational change of surfactant molecules enhance the visual understanding of the results obtained from characterization methods such as XRD and surface analysis of the organoclays. Batch experiments were carried out for the adsorption of p-chlorophenol (PCP) and different conditions (pH and temperature) were used in order to determine the optimum sorption. For comparison purpose, the experiments were repeated under the same conditions for p-nitrophenol (PNP). Langmuir and Freundlich equations were applied to the adsorption isotherm of PCP and PNP. The Freundlich isotherm model was found to be the best fit for both of the phenolic compounds. This involved multilayer adsorptions in the adsorption process. In particular, the binding affinity value of PNP was higher than that of PCP and this is attributable to their hydrophobicities. The adsorption of the phenolic compounds by organoclays intercalated with highly loaded surfactants was markedly improved possibly due to the fact that the intercalated surfactant molecules within the interlayer space contribute to the partition phases, which result in greater adsorption of the organic pollutants.

Developing academic and intercultural competence : the impact of a Patches program

This symposium focuses on an innovative Patches program that addresses imperatives with respect to the development of intercultural competence. The term, Patches, in this project refers to writing tasks and intercultural activities wherein each task becomes a ‘patch’ that eventually creates a quilt of learning as experienced by 58 second year BEd students from Malaysia and 14 fourth year domestic (Australian) BEd students. We take intercultural competence to mean students “ability to communicate effectively and appropriately in intercultural situations based on [their] intercultural knowledge, skills and attitudes” (Deardorff, 2006). The papers in this symposium provide detailed information about the design of the program, its impact on students’ perceptions of themselves as students, writers, and emerging professionals, and students’ development of intercultural competence.

Strategies for gaining and maintaining academic support for the institutional open access repository

The impact of research can be measured by use or citation count. The more widely available that research outputs are; the more likely they are to be used, and the higher the impact. Making the author-manuscript version of research outputs freely available via the institutional repository greatly increases the availability of research outputs and can increase the impact. QUT ePrints, the open access institutional repository of research outputs at Queensland University of Technology (QUT), Australia, was established in 2003 and is managed by the QUT Library. The repository now contains over 39,000 records. More than 21,000 of these records have full-text copies attached as result of continuous effort to maintain momentum and encourage academic engagement. The full-text deposit rate has continued to increase over time and, in 2012 (August, at the time of writing), 88% of the records for works published in 2012 provide access to a full-text copy. Achieving success has required a long term approach to collaboration, open access advocacy, repository promotion, support for the deposit process, and ongoing system development. This paper discusses the various approaches adopted by QUT Library, in collaboration with other areas of the University, to achieve success. Approaches include mainstreaming the repository via having it report to the University Research and Innovation Committee; regular provision of deposit rate data to faculties; championing key academic supporters; and holding promotional competitions and events such as during Open Access Week. Support and training is provided via regular deposit workshops with academics and faculty research support groups and via the provision of online self-help information. Recent system developments have included the integration of citation data (from Scopus and Web of Science) and the development of a statistical reporting system which incentivise engagement.

Knowledge unlatched : towards an open and networked future for academic publishing

Specialist book length publications in the humanities and social sciences (including but not exclusively monographs) are experiencing a crisis. It is clear that the current publishing system is failing both the producers and users of scholarship and neglects many of the opportunities associated with networked culture.

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.

Academic success in context-based chemistry : Demonstrating fluid transitions between concepts and context

Curriculum developers and researchers have promoted context-based programmes to arrest waning student interest and participation in the enabling sciences at high school and university. Context-based programmes aim for student connections between scientific discourse and real-world contexts to elevate curricular relevance without diminishing conceptual understanding. This interpretive study explored the learning transactions in one 11th grade context-based chemistry classroom where the context was the local creek. The dialectic of agency/structure was used as a lens to examine how the practices in classroom interactions afforded students the agency for learning. The results suggest that first, fluid transitions were evident in the student–student interactions involving successful students; and second, fluid transitions linking concepts to context were evident in the students’ successful reports. The study reveals that the structures of writing and collaborating in groups enabled students’ agential and fluent movement between the field of the real-world creek and the field of the formal chemistry classroom. Furthermore, characteristics of academically successful students in context-based chemistry are highlighted. Research, teaching, and future directions for context-based science teaching are discussed.