Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Relating vehicle generated pollutants to urban stormwater quality

Rapid urbanisation and resulting continuous increase in traffic has been recognised as key factors in the contribution of increased pollutant loads to urban stormwater and in turn to receiving waters. Urbanisation primarily increases anthropogenic activities and the percentage of impervious surfaces in urban areas. These processes are collectively responsible for urban stormwater pollution. In this regard, urban traffic and land use related activities have been recognised as the primary pollutant sources. This is primarily due to the generation of a range of key pollutants such as solids, heavy metals and PAHs. Appropriate treatment system design is the most viable approach to mitigate stormwater pollution. However, limited understanding of the pollutant process and transport pathways constrains effective treatment design. This highlights necessity for the detailed understanding of traffic and other land use related pollutants processes and pathways in relation to urban stormwater pollution. This study has created new knowledge in relation to pollutant processes and transport pathways encompassing atmospheric pollutants, atmospheric deposition and build-up on ground surfaces of traffic generated key pollutants. The research study was primarily based on in-depth experimental investigations. This thesis describes the extensive knowledge created relating to the processes of atmospheric pollutant build-up, atmospheric deposition and road surface build-up and establishing their relationships as a chain of processes. The analysis of atmospheric deposition revealed that both traffic and land use related sources contribute total suspended particulate matter (TSP) to the atmosphere. Traffic sources become dominant during weekdays whereas land use related sources become dominant during weekends due to the reduction in traffic sources. The analysis further concluded that atmospheric TSP, polycyclic aromatic hydrocarbons (PAHs) and heavy metals (HMs) concentrations are highly influenced by total average daily heavy duty traffic, traffic congestion and the fraction of commercial and industrial land uses. A set of mathematical equation were developed to predict TSP, PAHs and HMs concentrations in the atmosphere based on the influential traffic and land use related parameters. Dry deposition samples were collected for different antecedent dry days and wet deposition samples were collected immediately after rainfall events. The dry deposition was found to increase with the antecedent dry days and consisted of relatively coarser particles (greater than 1.4 ìm) when compared to wet deposition. The wet deposition showed a strong affinity to rainfall depth, but was not related to the antecedent dry period. It was also found that smaller size particles (less than 1.4 ìm) travel much longer distances from the source and deposit mainly with the wet deposition. Pollutants in wet deposition are less sensitive to the source characteristics compared to dry deposition. Atmospheric deposition of HMs is not directly influenced by land use but rather by proximity to high emission sources such as highways. Therefore, it is important to consider atmospheric deposition as a key pollutant source to urban stormwater in the vicinity of these types of sources. Build-up was analysed for five different particle size fractions, namely, <1 ìm, 1-75 ìm, 75-150 ìm, 150-300 ìm and >300 ìm for solids, PAHs and HMs. The outcomes of the study indicated that PAHs and HMs in the <75 ìm size fraction are generated mainly by traffic related activities whereas the > 150 ìm size fraction is generated by both traffic and land use related sources. Atmospheric deposition is an important source for HMs build-up on roads, whereas the contribution of PAHs from atmospheric sources is limited. A comprehensive approach was developed to predict traffic and other land use related pollutants in urban stormwater based on traffic and other land use characteristics. This approach primarily included the development of a set of mathematical equations to predict traffic generated pollutants by linking traffic and land use characteristics to stormwater quality through mathematical modelling. The outcomes of this research will contribute to the design of appropriate treatment systems to safeguard urban receiving water quality for future traffic growth scenarios. The „real world. application of knowledge generated was demonstrated through mathematical modelling of solids in urban stormwater, accounting for the variability in traffic and land use characteristics.

Influence of organic matter in road deposited particulates in heavy metal accumulation and transport

The research study discussed in the paper investigated the influence of organic matter on heavy metal adsorption for different particle size ranges of build-up solids. Samples collected from road surfaces were assessed for organic matter content, mineral composition, particle size distribution and effective cation exchange capacity. It was found that the organic matter plays a key role in >75µm particles in the adsorption of Zinc, Lead, Nickel and Copper, which are generated by traffic activities. Clay forming minerals and metal oxides of Iron, Aluminium and Manganese was found to be important for heavy metal adsorption to <75µm particles. It was also found that heavy metals adsorbed to organic matter are strongly bound to particles and these metal ions will not be bio-available if the chemical quality of the media remains stable.

Gender differences in recreational and transport cycling : a cross-sectional mixed-methods comparison of cycling patterns, motivators, and constraints

Background: Gender differences in cycling are well-documented. However, most analyses of gender differences make broad comparisons, with few studies modeling male and female cycling patterns separately for recreational and transport cycling. This modeling is important, in order to improve our efforts to promote cycling to women and men in countries like Australia with low rates of transport cycling. The main aim of this study was to examine gender differences in cycling patterns and in motivators and constraints to cycling, separately for recreational and transport cycling. Methods: Adult members of a Queensland, Australia, community bicycling organization completed an online survey about their cycling patterns; cycling purposes; and personal, social and perceived environmental motivators and constraints (47% response rate). Closed and open-end questions were completed. Using the quantitative data, multivariable linear, logistic and ordinal regression models were used to examine associations between gender and cycling patterns, motivators and constraints. The qualitative data were thematically analysed to expand upon the quantitative findings. Results: In this sample of 1862 bicyclists, men were more likely than women to cycle for recreation and for transport, and they cycled for longer. Most transport cycling was for commuting, with men more likely than women to commute by bicycle. Men were more likely to cycle on-road, and women off-road. However, most men and women did not prefer to cycle on-road without designed bicycle lanes, and qualitative data indicated a strong preference by men and women for bicycle-only off-road paths. Both genders reported personal factors (health and enjoyment related) as motivators for cycling, although women were more likely to agree that other personal, social and environmental factors were also motivating. The main constraints for both genders and both cycling purposes were perceived environmental factors related to traffic conditions, motorist aggression and safety. Women, however, reported more constraints, and were more likely to report as constraints other environmental factors and personal factors. Conclusion: Differences found in men’s and women’s cycling patterns, motivators and constraints should be considered in efforts to promote cycling, particularly in efforts to increase cycling for transport.

Methodology to assess safety effects of future Intelligent Transport Systems on railway level crossings

There is consistent evidence showing that driver behaviour contributes to crashes and near miss incidents at railway level crossings (RLXs). The development of emerging Vehicle-to-Vehicle and Vehicle-to-Infrastructure technologies is a highly promising approach to improve RLX safety. To date, research has not evaluated comprehensively the potential effects of such technologies on driving behaviour at RLXs. This paper presents an on-going research programme assessing the impacts of such new technologies on human factors and drivers’ situational awareness at RLX. Additionally, requirements for the design of such promising technologies and ways to display safety information to drivers were systematically reviewed. Finally, a methodology which comprehensively assesses the effects of in-vehicle and road-based interventions warning the driver of incoming trains at RLXs is discussed, with a focus on both benefits and potential negative behavioural adaptations. The methodology is designed for implementation in a driving simulator and covers compliance, control of the vehicle, distraction, mental workload and drivers’ acceptance. This study has the potential to provide a broad understanding of the effects of deploying new in-vehicle and road-based technologies at RLXs and hence inform policy makers on safety improvements planning for RLX.

Public realm and transport, international best practice case studies and opportunities for Brisbane

This report was prepared for Lat 27 Pty Ltd for the purpose of conducting a City Centre Public Realm and Active Transport Study for Urban Renewal Brisbane, Brisbane City Council. In this review, we highlight some key learnings and recommendations from innovative projects across the globe to inform public realm design and help facilitate active transport in subtropical Brisbane. Traditionally, Australian cities have been have been based on northern European models. This report is informed by the view that planners and urban designers must look beyond that paradigm to redefine and re-conceptualise our city in a different way, one that values our unique local identity and climate. In re-designing Brisbane’s public realm, therefore, design interventions and responses must celebrate our unique identity and outdoor lifestyle and address the subtropical climate's reality of life in warm humid summers and cool dry winters. The current period of rapid urban change, and the imperative to adapt to climate change, together offer an opportunity to prioritise and integrate design features that provide shade and shelter from sun and summer rain, open and permeable urban environments that facilitate cooling air movement, and connections to water and nature, so that the urban built form co-exists within an inviting, functional and memorable natural landscape. To inform this transformation, this review provides insight into international experiences and best practices. To date, although there is much practice-based knowledge, academic studies outlining learnings and recommendations from case studies (especially in a subtropical context) remain rare. Thus, a range of sources (industry reports, websites, journal articles and books) have been utilised.

Pervasive technology and public transport : opportunities beyond telematics

The advancements of technology in the field of public transport have been considerable. Information Technology (IT) has made the dissemination of information effortless, contributing to reduced perceived waiting time, increased sense of security, and value for money. Nevertheless, and in light of the ever more obvious widespread presence of powerful mobile devices, it seems that the use of technology may be geared towards supplementary services other than telematics. Looking at it from a passenger’s perspective, this article provides an overview of what IT-based services are currently offered in public transport and what is their assessed impact. We finalise by putting forward possible directions that future services might follow, and stress out the necessity to come up with frameworks that enable for the impact assessment on service quality and customer satisfaction.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Family violence or woman abuse? Putting gender back into the Canadian research equation

Research on violence against women has been among the most scrutinized areas in social science. From the beginning, efforts to empirically document the prevalence, incidence, and characteristics of violence against women have been hotly debated (DeKeseredy, 2011; Dragiewicz & DeKeseredy, forthcoming; Minaker & Snider, 2006). Objections that violence against women was rare have given way to acknowledgement that it is more common than once thought. Research on the outcomes of woman abuse has documented the serious ramifications of this type of violence for individual victims and the broader community. However, violence against women was not simply “discovered” by scholars in the 1960s, leading to a progressive growth of the literature. Knowledge production around violence against women has been fiercely contested, and feminist insights in particular have always been met with backlash(Gotell, 2007; Minkaer & Snider, 2006; Randall, 1989; Sinclair, 2003)...