Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Phase two of the National Credit Reforms : examining the regulation of payday lenders

This study seeks to analyse the adequacy of the current regulation of the payday lending industry in Australia, and consider whether there is a need for additional regulation to protect consumers of these services. The report examines the different regulatory approaches adopted in comparable OECD countries, and reviews alternative models for payday regulation, in particular, the role played by responsible lending. The study also examines the consumer protection mechanisms now in existence in Australia in the National Consumer Credit Protection Act 2009 (Cth) (NCCP) and the National Credit Code (NCC) contained in Schedule 1 of that Act and in the Australian Securities and Investments Commission Act 2001 (Cth).

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the friction pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71, and 9.81 m/s2 corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly-slug and slug-annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of dropset entrainment, higher superficial gas velocity was obtained at higher gravity level.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Footwear modifies coronal plane forefoot and sagittal plane hallux kinematics during stance phase of walking gait

Footwear is designed to reduce injury, and enhance performance. However, the effect footwear has on foot and ankle kinematics currently remains unknown. Acknowledging the need for improved understanding, multi-segment models of the foot-shoe complex need to be established to both describe and quantify the effect footwear has on the foot and ankle during stance phase of gait. The purpose of this study was to quantify how footwear alters the kinematics of the foot inside the shoe during stance phase of walking gait.

Footwear modifies foot and ankle kinematics during stance phase of walking gait

Footwear is designed to reduce injury and enhance performance. However, the effect footwear has on foot and ankle kinematics currently remains unknown. Acknowledging the need for improved understanding, the aim of this study was to describe the effect footwear has on the kinematics of a multi segment foot during stance phase of walking gait.

Diffusion determinants for passive building technologies

This summary is based on an international review of leading peer reviewed journals, in both technical and management fields. It draws on highly cited articles published between 2000 and 2009 to investigate the research question, "What are the diffusion determinants for passive building technologies in Australia?". Using a conceptual framework drawn from the innovation systems literature, this paper synthesises and interprets the literature to map the current state of passive building technologies in Australia and to analyse the drivers for, and obstacles to, their optimal diffusion. The paper concludes that the government has a key role to play through its influence over the specification of building codes.

Project 2.7 Leveraging R&D Investment for the Australian built environment : Phase 2 Case Study Reports Part 1 - Overview of Findings

This report provides an overview of findings of qualitative research comprising three case studies undertaken as a part of the retrospective analysis component of Sustainable Built Environment National Research Centre (SBEnrc) Project 2.7 Leveraging R&D investment for the Australian Built Environment. These case studies (see Parts 2, 3 and 4 of this suite of reports) were undertaken to illustrate the nature of past R&D investments in Australia. This was done to complement: (i) the audit and analysis of past R&D investment undertaken by Thomas Barlow (2011); and (ii) the Construction 2030 roadmap being developed by Swinburne University of Technology and Professor Göran Roos from VTT Technical Research Centre of Finland. These documents will be the basis for the final phase of the present project - developing policy guidelines for future R&D investment in the Australian built environment. Refer also Parts 1, 2 and 3 for detail findings.

Project 2.7 Leveraging R&D Investment for the Australian built environment : Phase 2 Case Study Report Part 4 - CADD, BIM and IPD

This report discusses findings of a case study into "CADD, BIM and IPD" undertaken as a part of the retrospective analysis component of Sustainable Built Environment National Research Centre (SBEnrc) Project 2.7 Leveraging R&D investment for the Australian Built Environment. This case study investigated the evolution that has taken place in the Queensland Department of Public Works Division of Project Services during the last 20 years from: the initial implementation of computer aided design and documentation(CADD); to the experimentation with building information modelling (BIM) from the mid 2000’s; embedding integrated practice (IP); to current steps towards integrated project delivery (IPD) with the integration of contractors in the design/delivery process. This case study should be read in conjunction with Part 1 of this suite of reports.

Project 2.7 Leveraging R&D Investment for the Australian built environment : Phase 2 Case Study Report Part 2 - Road Construction Safety

This report discusses findings of a case study into "Road Construction Safety" undertaken as a part of the retrospective analysis component of Sustainable Built Environment National Research Centre (SBEnrc) Project 2.7 Leveraging R&D investment for the Australian Built Environment. The Queensland Department of Transport and Main Roads (QTMR) has taken a leadership role in developing a safer working environment for road construction workers. In the past decades, a range of initiatives have been introduced to contribute to improved performance in this area. Several initiatives have been undertaken by QTMR as part of their overarching commitment to safety. Three such initiatives form the basis for this case study investigation, in order to better illustrate the nature of R&D investment and its impact on day-to-day operations and the supply chain. These are the development and implementation of: (i) the Mechanical Traffic Aid: (ii) the Thermal Imaging Camera; and (iii) the Trailer-based CCTV (camera). This case study should be read in conjunction with Part 1 of this suite of reports.

Project 2.7 Leveraging R&D Investment for the Australian built environment : Phase 2 Case Study Report Part 3 - Green Buildings

This report discusses findings of a case study into "Green Buildings" undertaken as a part of the retrospective analysis component of Sustainable Built Environment National Research Centre (SBEnrc) Project 2.7 Leveraging R&D investment for the Australian Built Environment. The Western Australian Government (WAG) has taken a leadership role for a number of decades in developing more environmentally responsive buildings. In the past decade, considerable initiatives have been introduced to contribute to: (i) greening the stock of government buildings; and (ii) providing leadership in the development of other non-residential buildings developed commercially. This role has been informed by global, national and internal initiatives and research in this area. This case study investigates: (i) the nature of this leadership; and (ii) the role of R&D policy development; and (iii) the dissemination and impact of outcomes in the broader industry. This case study should be read in conjunction with Part 1 of this suite of reports.