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.

Effects of rice husk biochar and sugar-mill by-products on methane consumption from two different soils

Methane (CH4) is an important greenhouse gas with a global warming potential (GWP) 25 times greater than carbon dioxide (CO2) that can be produced or consumed in soils depending on environmental conditions and other factors. Biochar application to soils has been shown to reduce CH4 emissions and to increase CH4 consumption. However, the effects of rice husk biochar (RB) have not been thoroughly investigated. Two 60-day laboratory incubation experiments were conducted to investigate the effects of amending two soil types with RB, raw mill mud (MM) and composted mill mud (CM) on soil CH4 consumption and emissions. Soil cores incubated in 1 L glass jars and gas samples were analysed for CH4 using gas chromatography. Average CH4 consumption rates varied from -0.06 to -0.68 g CH4-C( )/ha/d in sandy loam soil and -0.59 to -1.00 g CH4-C/ha/d in clay soil. Application of RB resulted in CH4 uptake of -0.52 to -0.55 g CH4-C/ha/d in sandy loam and -0.76 to -0.91 g CH4-C/ha/d in clay soil. Addition of MM showed low CH4 emissions or consumption at 60% water-filled pore space (WFPS) in both soils. However, at high water contents (>75% WFPS) the application of MM produced high rates of CH4 emissions which were significantly suppressed when RB was added. Cumulative emissions of the MM treatment produced 108.9 g CH4-C/ha at 75% WFPS and 11 459.3 g CH4-C/ha at 90% WFPS in sandy loam soil over a period of 60 days. RB can increase CH4 uptake under low soil water content (SWC) and decrease CH4 emissions under anaerobic conditions. CM expressed more potential to reduce CH4 emissions than those of MM.

Does experience with one type of two-wheeler affect behaviours and attitudes to other types?

Failure to give way by motor vehicles is a factor in many collisions with both powered and unpowered two wheelers (TWs). Motor vehicle drivers often report that they did not see the TW, but research has shown that motor vehicle drivers who have experience riding a motorcycle are less likely to fail to detect motorcycles. The research reported here examines whether this phenomenon extends to detection of bicycles and whether car drivers who have experience with one mode of TW show improved detection of the other mode. A driving simulator study was conducted in an Australian urban setting which incorporated some of the most common car-TW crash scenarios. Participants with car-only, car plus motorcycle, car plus bicycle, and car plus bicycle plus motorcycle experience operated a car simulator. Their interactions with both types of TWs were measured in terms of visual detection, lateral distance and speed when approaching and passing. The effects of different levels of colour and lighting of the TWs on driver responses were also examined. The attitudes of participants towards TWs were measured in a questionnaire.

Media pressures and corporate disclosure of social responsibility performance information : a study of two global clothing and sports retail companies

This paper investigates the social and environmental disclosure practices of two large multinational companies, specifically Nike and Hennes&Mauritz. Utilising a joint consideration of legitimacy theory and media agenda setting theory, we investigate the linkage between negative media attention, and positive corporate social and environmental disclosures. Our results generally support a view that for those industry‐related social and environmental issues attracting the greatest amount of negative media attention, these corporations react by providing positive social and environmental disclosures. The results were particularly significant in relation to labour practices in developing countries – the issue attracting the greatest amount of negative media attention for the companies in question.

Sources of ultrafine particles and chemical species along a traffic corridor : comparison of the results from two receptor models

Particulate matter is common in our environment and has been linked to human health problems particularly in the ultrafine size range. A range of chemical species have been associated with particulate matter and of special concern are the hazardous chemicals that can accentuate health problems. If the sources of such particles can be identified then strategies can be developed for the reduction of air pollution and consequently, the improvement of the quality of life. In this investigation, particle number size distribution data and the concentrations of chemical species were obtained at two sites in Brisbane, Australia. Source apportionment was used to determine the sources (or factors) responsible for the particle size distribution data. The apportionment was performed by Positive Matrix Factorisation (PMF) and Principal Component Analysis/Absolute Principal Component Scores (PCA/APCS), and the results were compared with information from the gaseous chemical composition analysis. Although PCA/APCS resolved more sources, the results of the PMF analysis appear to be more reliable. Six common sources identified by both methods include: traffic 1, traffic 2, local traffic, biomass burning, and two unassigned factors. Thus motor vehicle related activities had the most impact on the data with the average contribution from nearly all sources to the measured concentrations higher during peak traffic hours and weekdays. Further analyses incorporated the meteorological measurements into the PMF results to determine the direction of the sources relative to the measurement sites, and this indicated that traffic on the nearby road and intersection was responsible for most of the factors. The described methodology which utilised a combination of three types of data related to particulate matter to determine the sources could assist future development of particle emission control and reduction strategies.

Comparison of two suspension control strategies for multi-axle heavy truck

Two simple and effective control strategies for a multi-axle heavy truck, modified skyhook damping (MSD) control and proportional-integration-derivative (PID) control, were implemented into functional virtual prototype (FVP) model and compared in terms of road friendliness and ride comfort. A four-axle heavy truck-road coupling system model was established using FVP technology and validated through a ride comfort test. Then appropriate passive air suspensions were chosen to replace the rear tandem suspensions of the original truck model for preliminary optimization. The mechanical properties and time lag of dampers were taken into account in simulations of MSD and PID semi-active dampers implemented using MATLAB/Simulink. Through co-simulations with Adams and MATLAB, the effects of semi-active MSD and PID control were analyzed and compared, and control parameters which afforded the best comprehensive performance for each control strategy were chosen. Simulation results indicate that compared with the passive air suspension truck, semi-active MSD control improves both ride comfort and road-friendliness markedly, with optimization ratios of RMS vertical acceleration and RMS tyre force ranging from 10.1% to 44.8%. However, semi-active PID control only reduces vertical vibration of the driver’s seat by 11.1%, 11.1% and 10.9% on A, B and C level roads respectively. Both strategies are robust to the variation of road level.

Social adjustment and symptomatology in two types of homeless adolescents : runaways and throwaways

Previous research on homeless adolescents has largely ignored the distinction between those who have left home on their volition (runaways) and those who have been forced to leave (throwaways). Fifty-two homeless adolescents in Brisbane, Australia, were assessed to compare male and female runaways and throwaways for social adjustment and symptomatology. Differences for social adjustment (antisocial tendencies and aggression) and symptomatology (social isolation and depression) were predicted. Results indicated that male runaways were significantly more hostile than male throwaways (p < 0,001), and significantly more socially isolated than female runaways (p < 0,025). Female throwaways, however, were significantly more hostile than male throwaways (p < 0,025) and female runaways (p < 0,025). Yet homeless males overall had a significantly stronger urge to act out hostility than homeless females (p < 0,025). In addition, female throwaways were significantly more antisocial than male throwaways (p < 0,001). There were no significant differences for depression. A theory of inner social control (Hirschi, 1969), postulating absence of bonding in earlier socialization, was supported.

The enactment of formative assessment in English language classrooms in two Chinese universities : teacher and student responses

The College English Curriculum Requirements (CECR), announced by the Chinese Ministry of Education in 2007, recommended the inclusion of formative assessment into the existing summative assessment framework of College English. This policy had the potential to fundamentally change the nature of assessment and its role in the teaching and learning of English in Chinese universities. In order to document and analyse these changes, case studies involving English language teachers and learners were undertaken in two Chinese Universities: one a Key university in the national capital; the other a non-Key university in a western province. The case study design incorporated classroom observations and interviews with English language teachers and their students. The type and focus of feedback and the engagement of students in assessment were analysed in the two contexts. Fundamental to the analysis was the concept of enactment, with the focus of this study on the ways that policy ideas and principles were enacted in the practices of the Chinese university classroom. Understandings of formative assessment as applied in contexts other than the predominantly Western, Anglophone contexts from where many of its principles derive, are offered.

Handbook on the Knowledge Economy : Volume Two

The second volume of the Handbook on the Knowledge Economy is a worthy companion to the highly successful original volume published in 2005, extending its theoretical depth and developing its coverage. Together the two volumes provide the single best work and reference point for knowledge economy studies. The second volume with fifteen original essays by renowned scholars in the field, provides insightful and robust analyses of the development potential of the knowledge economy in all its aspects, forms and manifestations.

Condition-based maintenance optimisation without a predetermined strategy structure for a two-component series system

Most existing research on maintenance optimisation for multi-component systems only considers the lifetime distribution of the components. When the condition-based maintenance (CBM) strategy is adopted for multi-component systems, the strategy structure becomes complex due to the large number of component states and their combinations. Consequently, some predetermined maintenance strategy structures are often assumed before the maintenance optimisation of a multi-component system in a CBM context. Developing these predetermined strategy structure needs expert experience and the optimality of these strategies is often not proofed. This paper proposed a maintenance optimisation method that does not require any predetermined strategy structure for a two-component series system. The proposed method is developed based on the semi-Markov decision process (SMDP). A simulation study shows that the proposed method can identify the optimal maintenance strategy adaptively for different maintenance costs and parameters of degradation processes. The optimal maintenance strategy structure is also investigated in the simulation study, which provides reference for further research in maintenance optimisation of multi-component systems.

A revision of Calyptochloa C.E.Hubb. (Poaceae), with two new species and a new subspecies

Thompson, E.J. & Simon, B.K. (2012). A revision of Calyptochloa C.E.Hubb. (Poaceae), with two new species and a new subspecies. Austrobaileya 8(4): 634–652. Two new species of Calyptochloa C.E.Hubb. (Calyptochloa cylindrosperma E.J.Thomps. & B.K.Simon and C. johnsoniana E.J.Thomps. & B.K.Simon) endemic to central Queensland, and a new subspecies of Calyptochloa gracillima C.E.Hubb. (C. gracillima subsp. ipsviciensis E.J.Thomps. & B.K.Simon) endemic to southeast Queensland are described and illustrated.

A new model to study healing of a complex femur fracture with concurrent soft tissue injury in sheep

High energy bone fractures resulting from impact trauma are often accompanied by subcutaneous soft tissue injuries, even if the skin remains intact. There is evidence that such closed soft tissue injuries affect the healing of bone fractures, and vice versa. Despite this knowledge, most impact trauma studies in animals have focussed on bone fractures or soft tissue trauma in isolation. However, given the simultaneous impact on both tissues a better understanding of the interaction between these two injuries is necessary to optimise clinical treatment. The aim of this study was therefore to develop a new experimental model and characterise, for the first time, the healing of a complex fracture with concurrent closed soft tissue trauma in sheep. A pendulum impact device was designed to deliver a defined and standardised impact to the distal thigh of sheep, causing a reproducible contusion injury to the subcutaneous soft tissues. In a subsequent procedure, a reproducible femoral butterfly fracture (AO C3-type) was created at the sheep’s femur, which was initially stabilised for 5 days by an external fixator construct to allow for soft tissue swelling to recede, and ultimately in a bridging construct using locking plates. The combined injuries were applied to twelve sheep and the healing observed for four or eight weeks (six animals per group) until sacrifice. The pendulum impact led to a moderate to severe circumferential soft tissue injury with significant bruising, haematomas and partial muscle disruptions. Posttraumatic measurements showed elevated intra-compartmental pressure and circulatory tissue breakdown markers, with recovery to normal, pre-injury values within four days. Clinically, no neurovascular deficiencies were observed. Bi-weekly radiological analysis of the healing fractures showed progressive callus healing over time, with the average number of callus bridges increasing from 0.4 at two weeks to 4.2 at eight weeks. Biomechanical testing after sacrifice showed increasing torsional stiffness between four and eight weeks healing time from 10% to 100%, and increasing ultimate torsional strength from 10% to 64% (relative to the contralateral control limb). Our results demonstrate the robust healing of a complex femur fracture in the presence of a severe soft tissue contusion injury in sheep and demonstrate the establishment of a clinically relevant experimental model, for research aimed at improving the treatment of bone fractures accompanied by closed soft tissue injuries.

A Tale of Two Marinas

A Tale of Two Marinas: Burnett Heads and Port of Bundaberg This exhibition showcases the work of 4th Year undergraduate Landscape Architecture and Civil and Environmental Engineering students in response to issues of sustainability in Burnett Heads and the Port of Bundaberg. The Burnett Heads & Port of Bundaberg project site, just north of Bargara, is a complex mix of port facilities, urban development, established residential and service areas, coastal conservation and agriculture. The project brief was to prepare a range of strategic planning and environmental management options for future urban and infrastructure development. 4th year undergraduate Landscape Architecture and Civil and Environmental Engineering students worked over one teaching semester with guidance from QUT academics and partner organisations to produce strategic planning, environmental management planning and design options for managing future growth in the area. The project process involved three visits to the site by QUT students and staff. The first visit at the project’s commencement included a formal briefing session with project partners the Burnett Mary Regional Group, Port of Brisbane Corporation, and Queensland Department of Local Government and Planning. Formal and informal community engagement facilitated by the Burnett Heads Progress Association also allowed students to gain some understanding of local values. A second visit mid-project involved a ‘Futures Workshop’ with students and community. This enabled the students to gain the benefit of local knowledge and experience in response to their work-in-progress, and to establish priorities for project completion. It strengthened the relationship between the community and the students. A final exhibition, ‘A Tale of Two Marinas’ was held at the Burnett Progress Hall just prior to completion of the project. The student work exhibited offers a diverse number of alternative options for the future urban development, infrastructure and environmental planning that the partner organisations have used for ongoing consultation.