Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

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.

Bus and car travel time on urban networks : integrating Bluetooth and bus vehicle identification data

Travel time in an important transport performance indicator. Different modes of transport (buses and cars) have different mechanical and operational characteristics, resulting in significantly different travel behaviours and complexities in multimodal travel time estimation on urban networks. This paper explores the relationship between bus and car travel time on urban networks by utilising the empirical Bluetooth and Bus Vehicle Identification data from Brisbane. The technologies and issues behind the two datasets are studied. After cleaning the data to remove outliers, the relationship between not-in-service bus and car travel time and the relationship between in-service bus and car travel time are discussed. The travel time estimation models reveal that the not-in-service bus travel time are similar to the car travel time and the in-service bus travel time could be used to estimate car travel time during off-peak hours

Adaptive metering algorithm for electronic commercial vehicle preclearance systems

This paper presents an adaptive metering algorithm for enhancing the electronic screening (e-screening) operation at truck weight stations. This algorithm uses a feedback control mechanism to control the level of truck vehicles entering the weight station. The basic operation of the algorithm allows more trucks to be inspected when the weight station is underutilized by adjusting the weight threshold lower. Alternatively, the algorithm restricts the number of trucks to inspect when the station is overutilized to prevent queue spillover. The proposed control concept is demonstrated and evaluated in a simulation environment. The simulation results demonstrate the considerable benefits of the proposed algorithm in improving overweight enforcement with minimal negative impacts on nonoverweighed trucks. The test results also reveal that the effectiveness of the algorithm improves with higher truck participation rates in the e-screening program.

Resilient Maroochydore 2029 : Urban Design Futures

Resilient Maroochydore 2029 This exhibition showcases the work of 4th year undergraduate Landscape Architecture students in response to issues of sustainability in Maroochydore on the Queensland Sunshine coast. The projects comprising this exhibition all investigate possible design futures for the Maroochydore Centre, in the light of a series of new disturbance scenarios. Specific disturbances upon the landscape have been imagined, and design resolutions developed based on resilience to these disturbances. The proposals investigate how the Maroochydore Centre might respond to these scenarios, and how future components of the Centre might be designed for greater ‘resilience’. The Exhibition Five groups of students (32 in total) produced five strategic planning and design options toward this future: Team Transect: “What happens to a region following a sustained period of economic prosperity, with affordable property and negligible unemployment? This proposal investigates the effects on a community of massive population explosion, land shortages and inadequate planning regulations following an extended boom period.” The Foodfighters: “This proposal considers the scenario of massive food shortages and of escalating prices, and the possibility of government intervention to stabilise food supply. Strategies based upon simplified, collaborative approaches to food production are investigated.” The TTMKG: “This proposal explores the scenario of Peak Oil and the subsequent effects on society of homelessness, large scale unemployment, food shortages and global financial and political instability. Individual opportunities are restricted by the limitations of bicycle transportation.” Team Peak: “Peak Oil has restricted private vehicle transport to only the most wealthy, while public transport systems are under immense pressure. Rising unemployment drives localised trade initiatives, and the global import/export market has collapsed. This proposal considers the transition of a community from its position in a global economy to that of a relocalised economy, where basic needs are secured as close to home as possible.” After the City: “A rapid population decline as a result of the region’s failing economy has resulted in a fragmented urban fabric. This proposal investigates the possibility of new suburbanisation, reinterpretation and reinvention of space through phased processes.”

Effects of eco-driving instructions using a vehicle with automatic transmission on urban roads

Eco-driving instructions could reduce fuel consumption to up to 20% (EcoMove, 2010). Participants (N=13) drove an instrumented vehicle (i.e. Toyota Camry 2007) with an automatic transmission. Fuel consumption of the participants were compared before and after they received eco-driving instructions. Participants drove the same vehicle on the same urban route under similar traffic conditions. Results show that, on free flow sections of the track, all participants drove slightly faster (on average, 0.7 Km/h faster), during the lap for which they were instructed to drive in an eco-friendly manner as compared to when they were not given the eco-driving instruction. Suprisingly, eco-driving instructions increased the RPM significantly in most cases. Fuel consumption slightly decreased (6%) after the eco-driving instructions. We have found strong evidence showing that the fuel saving observed in our experiment (urban environment, automatic transmission) fall short of the 20% reduction claimed in other international trials.

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.

The implications of cross-regional differences for the design of In-vehicle Information Systems : a comparison of Australian and Chinese drivers

The increasing global distribution of automobiles necessitates that the design of In-vehicle Information Systems (IVIS) is appropriate for the regions to which they are being exported. Differences between regions such as culture, environment and traffic context can influence the needs, usability and acceptance of IVIS. This paper describes two studies aimed at identifying regional differences in IVIS design needs and preferences across drivers from Australia and China to determine the impact of any differences on IVIS design. Using a questionnaire and interaction clinics, the influence of cultural values and driving patterns on drivers' preferences for, and comprehension of, surface- and interaction-level aspects of IVIS interfaces was explored. Similarities and differences were found between the two regional groups in terms of preferences for IVIS input control types and labels and in the comprehension of IVIS functions. Specifically, Chinese drivers preferred symbols and Chinese characters over English words and were less successful (compared to Australians) at comprehending English abbreviations, particularly for complex IVIS functions. Implications in terms of the current trend to introduce Western-styled interfaces into other regions with little or no adaptation are discussed.

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