Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Ambient temperature and cardiorespiratory morbidity : a systematic review and meta-analysis

BACKGROUND: The effect of extreme temperature has become an increasing public health concern. Evaluating the impact of ambient temperature on morbidity has received less attention than its impact on mortality. METHODS: We performed a systematic literature review and extracted quantitative estimates of the effects of hot temperatures on cardiorespiratory morbidity. There were too few studies on effects of cold temperatures to warrant a summary. Pooled estimates of effects of heat were calculated using a Bayesian hierarchical approach that allowed multiple results to be included from the same study, particularly results at different latitudes and with varying lagged effects. RESULTS: Twenty-one studies were included in the final meta-analysis. The pooled results suggest an increase of 3.2% (95% posterior interval = -3.2% to 10.1%) in respiratory morbidity with 1°C increase on hot days. No apparent association was observed for cardiovascular morbidity (-0.5% [-3.0% to 2.1%]). The length of lags had inconsistent effects on the risk of respiratory and cardiovascular morbidity, whereas latitude had little effect on either. CONCLUSIONS: The effects of temperature on cardiorespiratory morbidity seemed to be smaller and more variable than previous findings related to mortality.

Visualising the 48 hour game making challenge

We have always felt that “something very special” was happening in the 48hr and other similar game jams. This “something” is more than the intensity and challenge of the experience, although this certainly has appeal for the participants. We had an intuition that these intense 48 hour game jams exposed something pertinent to the changing shape of the Australian games industry where we see the demise of the late 20th century large studio - the “Night Elf” model and the growth of the small independent model. There are a large number of wider economic and cultural factors around this evolution but our interest is specifically in the change from “industry” to “creative industry” and the growth of games as a cultural media and art practice. If we are correct in our intuition, then illuminating this something also has important ramifications for those courses which teach game and interaction design and development. Rather than undertake a formal ethno-methodological approach, we decided to track as many of the actors in the event as possible. We documented the experience (Keith Novak’s beautiful B&W photography), the individual and their technology (IOGraph mouse tracking), the teams as a group (Time lapse photography) and movement tracking throughout the whole space (Blue tooth phone tracking). The raw data collected has given us opportunity to start a commentary on the “something special” happening in the 48hr.

Benefits of publicly available data

The National Morbidity, Mortality, and Air Pollution Study (NMMAPS) was designed to examine the health effects of air pollution in the United States. The primary question was whether particulate matter was responsible for the associations between air pollution and daily mortality. Secondary questions concerned measurement error in air pollution and mortality displacement.1 Since then, NMMAPS has been used to answer many important questions in environmental epidemiology...

Performing design analysis: game design creativity and the theatre of the impressed

We report and reflect upon the early stages of a research project that endeavours to establish a culture of critical design thinking in a tertiary game design course. We first discuss the current state of the Australian game industry and consider some perceived issues in game design courses and graduate outcomes. The second sec-tion presents our response to these issues: a project in progress which uses techniques originally exploited by Augusto Boal in his work, Theatre of the Oppressed. We appropriate Boal’s method to promote critical design thinking in a games design class. Finally, we reflect on the project and the ontology of design thinking from the perspective of Bruce Archer’s call to reframe design as a ‘third academic art’.

Exposure to hot and cold temperatures and ambulance attendances in Brisbane, Australia: A time series study

ABSTRACT Objectives: To investigate the effect of hot and cold temperatures on ambulance attendances. Design: An ecological time series study. Setting and participants: The study was conducted in Brisbane, Australia. We collected information on 783 935 daily ambulance attendances, along with data of associated meteorological variables and air pollutants, for the period of 2000–2007. Outcome measures: The total number of ambulance attendances was examined, along with those related to cardiovascular, respiratory and other non-traumatic conditions. Generalised additive models were used to assess the relationship between daily mean temperature and the number of ambulance attendances. Results: There were statistically significant relationships between mean temperature and ambulance attendances for all categories. Acute heat effects were found with a 1.17% (95% CI: 0.86%, 1.48%) increase in total attendances for 1 °C increase above threshold (0–1 days lag). Cold effects were delayed and longer lasting with a 1.30% (0.87%, 1.73%) increase in total attendances for a 1 °C decrease below the threshold (2–15 days lag). Harvesting was observed following initial acute periods of heat effects, but not for cold effects. Conclusions: This study shows that both hot and cold temperatures led to increases in ambulance attendances for different medical conditions. Our findings support the notion that ambulance attendance records are a valid and timely source of data for use in the development of local weather/health early warning systems.

Assessment of the health impacts of the 2011 summer floods in Brisbane

Background: During December 2010 and January 2011, torrential rainfall in Queensland resulted in the worst flooding in over 50 years. We carried out a community-based survey to assess the health impacts of this flooding in the city of Brisbane. Methods: A community-based survey was conducted in 12 flood-affected electorates using postal questionnaires. A random sample of residents in these areas was drawn from electoral rolls. Questions examined sociodemographic information, the direct impact of flooding on the household, and perceived flood-related health impacts. Outcome variables included perceived flood-related effects on overall and respiratory health, along with mental health outcomes measured by psychosocial distress, reduced sleep quality and probable post-traumatic stress disorder (PTSD). Multivariable logistic regression was used to examine the association between flooding and health outcome variables, adjusted for current health status and socioeconomic factors. Results: 3000 residents were invited to participate in this survey, with 960 responses (32%). People whose households were directly impacted by flooding had a decrease in perceived overall health (OR 5.3, 95% CI: 2.8–10.2), along with increases in psychological distress (OR 1.9, 1.1–3.5), decreased sleep quality (OR 2.3, 1.2–4.4), and probable PTSD (OR 2.3, 1.2–4.5). Residents were also more likely to increase usage of both tobacco (OR 6.3, 2.4–16.8) and alcohol (OR 7.0, 2.2–22.3) after flooding. Conclusions: There were significant impacts of flood events on residents’ health, in particular psychosocial health. Improved support strategies may need to be integrated into existing disaster management programs to reduce flood‐related health impacts.

Floods and human health : a systematic review

Floods are the most common type of disaster globally, responsible for almost 53,000 deaths in the last decade alone (23:1 low- versus high-income countries). This review assessed recent epidemiological evidence on the impacts of floods on human health. Published articles (2004–2011) on the quantitative relationship between floods and health were systematically reviewed. 35 relevant epidemiological studies were identified. Health outcomes were categorized into short- and long-term and were found to depend on the flood characteristics and people's vulnerability. It was found that long-term health effects are currently not well understood. Mortality rates were found to increase by up to 50% in the first year post-flood. After floods, it was found there is an increased risk of disease outbreaks such as hepatitis E, gastrointestinal disease and leptospirosis, particularly in areas with poor hygiene and displaced populations. Psychological distress in survivors (prevalence 8.6% to 53% two years post-flood) can also exacerbate their physical illness. There is a need for effective policies to reduce and prevent flood-related morbidity and mortality. Such steps are contingent upon the improved understanding of potential health impacts of floods. Global trends in urbanization, burden of disease, malnutrition and maternal and child health must be better reflected in flood preparedness and mitigation programs.

Exposure to hot and cold temperatures and ambulance attendances in Brisbane, Australia

Objectives: To investigate the effect of hot and cold temperatures on ambulance attendances. Design: An ecological time series study. Setting and participants: The study was conducted in Brisbane, Australia. We collected information on 783 935 daily ambulance attendances, along with data of associated meteorological variables and air pollutants, for the period of 2000–2007. Outcome measures: The total number of ambulance attendances was examined, along with those related to cardiovascular, respiratory and other non-traumatic conditions. Generalised additive models were used to assess the relationship between daily mean temperature and the number of ambulance attendances. Results: There were statistically significant relationships between mean temperature and ambulance attendances for all categories. Acute heat effects were found with a 1.17% (95% CI: 0.86%, 1.48%) increase in total attendances for 1 °C increase above threshold (0–1 days lag). Cold effects were delayed and longer lasting with a 1.30% (0.87%, 1.73%) increase in total attendances for a 1 °C decrease below the threshold (2–15 days lag). Harvesting was observed following initial acute periods of heat effects, but not for cold effects. Conclusions: This study shows that both hot and cold temperatures led to increases in ambulance attendances for different medical conditions. Our findings support the notion that ambulance attendance records are a valid and timely source of data for use in the development of local weather/health early warning systems.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. 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.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.