Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Modeling crash types: New insights into the effects of covariates on crashes at rural intersections

Many studies focused on the development of crash prediction models have resulted in aggregate crash prediction models to quantify the safety effects of geometric, traffic, and environmental factors on the expected number of total, fatal, injury, and/or property damage crashes at specific locations. Crash prediction models focused on predicting different crash types, however, have rarely been developed. Crash type models are useful for at least three reasons. The first is motivated by the need to identify sites that are high risk with respect to specific crash types but that may not be revealed through crash totals. Second, countermeasures are likely to affect only a subset of all crashes—usually called target crashes—and so examination of crash types will lead to improved ability to identify effective countermeasures. Finally, there is a priori reason to believe that different crash types (e.g., rear-end, angle, etc.) are associated with road geometry, the environment, and traffic variables in different ways and as a result justify the estimation of individual predictive models. The objectives of this paper are to (1) demonstrate that different crash types are associated to predictor variables in different ways (as theorized) and (2) show that estimation of crash type models may lead to greater insights regarding crash occurrence and countermeasure effectiveness. This paper first describes the estimation results of crash prediction models for angle, head-on, rear-end, sideswipe (same direction and opposite direction), and pedestrian-involved crash types. Serving as a basis for comparison, a crash prediction model is estimated for total crashes. Based on 837 motor vehicle crashes collected on two-lane rural intersections in the state of Georgia, six prediction models are estimated resulting in two Poisson (P) models and four NB (NB) models. The analysis reveals that factors such as the annual average daily traffic, the presence of turning lanes, and the number of driveways have a positive association with each type of crash, whereas median widths and the presence of lighting are negatively associated. For the best fitting models covariates are related to crash types in different ways, suggesting that crash types are associated with different precrash conditions and that modeling total crash frequency may not be helpful for identifying specific countermeasures.

Tamper evidence for heavy vehicle on board mass systems

On-board mass (OBM) monitoring devices on heavy vehicles (HVs) have been tested in a national programme jointly by Transport Certification Australia Limited and the National Transport Commission. The tests were for, amongst other parameters, accuracy and tamper-evidence. The latter by deliberately tampering with the signals from OBM primary transducers during the tests. The OBM feasibility team is analysing dynamic data recorded at the primary transducers of OBM systems to determine if it can be used to detect tamper events. Tamper-evidence of current OBM systems needs to be determined if jurisdictions are to have confidence in specifying OBM for HVs as part of regulatory schemes. An algorithm has been developed to detect tamper events. The results of its application are detailed here.

Assessing wet crashes for the skid resistance management of road assets

Australia, road crash trauma costs the nation A$15 billion annually whilst the US estimates an economic impact of around US$ 230 billion on its network. Worldwide economic cost of road crashes is estimated to be around US$ 518 billion each year. Road accidents occur due to a number of factors including driver behaviour, geometric alignment, vehicle characteristics, environmental impacts, and the type and condition of the road surfacing. Skid resistance is considered one of the most important road surface characteristics because it has a direct effect on traffic safety. In 2005, Austroads (the Association of Australian and New Zealand Road Transport and Traffic Authorities) published a guideline for the management of skid resistance and Queensland Department of Main Roads (QDMR) developed a skid resistance management plan (SRMP). The current QDMR strategy is based on rationale analytical methodology supported by field inspection with related asset management decision tools. The Austroads’s guideline and QDMR's skid resistance management plan have prompted QDMR to review its skid resistance management practice. As a result, a joint research project involving QDMR, Queensland University of Technology (QUT) and the Corporative Research Centre for Integrated Engineering Asset Management (CRC CIEAM) was formed. The research project aims at investigating whether there is significant relationship between road crashes and skid resistance on Queensland’s road networks. If there is, the current skid resistance management practice of QDMR will be reviewed and appropriate skid resistance investigatory levels will be recommended. This paper presents analysis results in assessing the relationship between wet crashes and skid resistance on Queensland roads. Attributes considered in the analysis include surface types, annual average daily traffic (AADT), speed and seal age.

Making space and place for the knowledge economy : knowledge-based development of Australian cities

The impact of what has been broadly labelled the knowledge economy has been such that, even in the absence of precise measurement, it is the undoubted dynamo of today’s global market, and an essential part of any global city. The socio-economic importance of knowledge production in a knowledge economy is clear, and it is an emerging social phenomenon and research agenda in geographical studies. Knowledge production, and where, how and by whom it is produced, is an urban phenomenon that is poorly understood in an era of strong urbanisation. This paper focuses on knowledge community precincts as the catalytic magnet infrastructures impacting on knowledge production in cities. The paper discusses the increasing importance of knowledge-based urban development within the paradigm of the knowledge economy, and the role of knowledge community precincts as instruments to seed the foundation of knowledge production in cities. This paper explores the knowledge based urban development, and particularly knowledge community precinct development, potentials of Sydney, Melbourne and Brisbane, and benchmarks this against that of Boston, Massachusetts.

Derivation of motor vehicle tailpipe particle emission factors suitable for modelling urban fleet emissions and air quality assessments

Background, aim, and scope Urban motor vehicle fleets are a major source of particulate matter pollution, especially of ultrafine particles (diameters < 0.1 µm), and exposure to particulate matter has known serious health effects. A considerable body of literature is available on vehicle particle emission factors derived using a wide range of different measurement methods for different particle sizes, conducted in different parts of the world. Therefore the choice as to which are the most suitable particle emission factors to use in transport modelling and health impact assessments presented as a very difficult task. The aim of this study was to derive a comprehensive set of tailpipe particle emission factors for different vehicle and road type combinations, covering the full size range of particles emitted, which are suitable for modelling urban fleet emissions. Materials and methods A large body of data available in the international literature on particle emission factors for motor vehicles derived from measurement studies was compiled and subjected to advanced statistical analysis, to determine the most suitable emission factors to use in modelling urban fleet emissions. Results This analysis resulted in the development of five statistical models which explained 86%, 93%, 87%, 65% and 47% of the variation in published emission factors for particle number, particle volume, PM1, PM2.5 and PM10 respectively. A sixth model for total particle mass was proposed but no significant explanatory variables were identified in the analysis. From the outputs of these statistical models, the most suitable particle emission factors were selected. This selection was based on examination of the statistical robustness of the statistical model outputs, including consideration of conservative average particle emission factors with the lowest standard errors, narrowest 95% confidence intervals and largest sample sizes, and the explanatory model variables, which were Vehicle Type (all particle metrics), Instrumentation (particle number and PM2.5), Road Type (PM10) and Size Range Measured and Speed Limit on the Road (particle volume). Discussion A multiplicity of factors need to be considered in determining emission factors that are suitable for modelling motor vehicle emissions, and this study derived a set of average emission factors suitable for quantifying motor vehicle tailpipe particle emissions in developed countries. Conclusions The comprehensive set of tailpipe particle emission factors presented in this study for different vehicle and road type combinations enable the full size range of particles generated by fleets to be quantified, including ultrafine particles (measured in terms of particle number). These emission factors have particular application for regions which may have a lack of funding to undertake measurements, or insufficient measurement data upon which to derive emission factors for their region. Recommendations and perspectives In urban areas motor vehicles continue to be a major source of particulate matter pollution and of ultrafine particles. It is critical that in order to manage this major pollution source methods are available to quantify the full size range of particles emitted for traffic modelling and health impact assessments.

Ions in motor vehicle exhaust and their dispersion near busy roads

Measurements in the exhaust plume of a petrol-driven motor car showed that molecular cluster ions of both signs were present in approximately equal amounts. The emission rate increased sharply with engine speed while the charge symmetry remained unchanged. Measurements at the kerbside of nine motorways and five city roads showed that the mean total cluster ion concentration near city roads (603 cm-3) was about one-half of that near motorways (1211 cm-3) and about twice as high as that in the urban background (269 cm-3). Both positive and negative ion concentrations near a motorway showed a significant linear increase with traffic density (R2=0.3 at p<0.05) and correlated well with each other in real time (R2=0.87 at p<0.01). Heavy duty diesel vehicles comprised the main source of ions near busy roads. Measurements were conducted as a function of downwind distance from two motorways carrying around 120-150 vehicles per minute. Total traffic-related cluster ion concentrations decreased rapidly with distance, falling by one-half from the closest approach of 2m to 5m of the kerb. Measured concentrations decreased to background at about 15m from the kerb when the wind speed was 1.3 m s-1, this distance being greater at higher wind speed. The number and net charge concentrations of aerosol particles were also measured. Unlike particles that were carried downwind to distances of a few hundred metres, cluster ions emitted by motor vehicles were not present at more than a few tens of metres from the road.

Making space and place for knowledge production : socio-spatial development of knowledge community precincts

In the knowledge era the importance of making space and place for knowledge production is clearly understood worldwide by many city administrations that are keen on restructuring their cities as highly competitive and creative places. Consequently, knowledge-based urban development and socio-spatial development of knowledge community precincts have taken their places among the emerging agendas of the urban planning and development practice. This chapter explores these emerging issues and scrutinizes the development of knowledge community precincts that have important economic, social and cultural dimensions on the formation of competitive and creative urban regions. The chapter also sheds light on the new challenges for planning discipline, and discusses the need for and some specifics of a new planning paradigm suitable for dealing with 21st Century’s socio-economic development and urbanization problems.

Distributed orthogonal space-time block codes with adaptive diversity gain

In this paper we present a novel distributed coding protocol for multi-user cooperative networks. The proposed distributed coding protocol exploits the existing orthogonal space-time block codes to achieve higher diversity gain by repeating the code across time and space (available relay nodes). The achievable diversity gain depends on the number of relay nodes that can fully decode the signal from the source. These relay nodes then form space-time codes to cooperatively relay to the destination using number of time slots. However, the improved diversity gain is archived at the expense of the transmission rate. The design principles of the proposed space-time distributed code and the issues related to transmission rate and diversity trade off is discussed in detail. We show that the proposed distributed space-time coding protocol out performs existing distributed codes with a variable transmission rate.

The embodied hybrid space : designing ubiquitous computing towards an amplification of situated real world experiences

The emergence of mobile and ubiquitous computing technology has created what is often referred to as the hybrid space – a virtual layer of digital information and interaction opportunities that sit on top of and augment the physical environment. Embodied media materialise digital information as observable and sometimes interactive parts of the physical environment. The aim of this work is to explore ways to enhance people’s situated real world experience, and to find out what the role and impact of embodied media in achieving this goal can be. The Edge, an initiative of the State Library of Queensland in Brisbane, Australia, and case study of this thesis, envisions to be a physical place for people to meet, explore, experience, learn and teach each other creative practices in various areas related to digital technology and arts. Guided by an Action Research approach, this work applies Lefebvre’s triad of space (1991) to investigate the Edge as a social space from a conceived, perceived and lived point of view. Based on its creators’ vision and goals on the conceived level, different embodied media are iteratively designed, implemented and evaluated towards shaping and amplifying the Edge’s visitor experience on the perceived and lived level.

The Heavy Vehicle Study : a case-control study investigating risk factors for crash in long distance heavy vehicle drivers in Australia

Background Heavy vehicle transportation continues to grow internationally; yet crash rates are high, and the risk of injury and death extends to all road users. The work environment for the heavy vehicle driver poses many challenges; conditions such as scheduling and payment are proposed risk factors for crash, yet the precise measure of these needs quantifying. Other risk factors such as sleep disorders including obstructive sleep apnoea have been shown to increase crash risk in motor vehicle drivers however the risk of heavy vehicle crash from this and related health conditions needs detailed investigation. Methods and Design The proposed case control study will recruit 1034 long distance heavy vehicle drivers: 517 who have crashed and 517 who have not. All participants will be interviewed at length, regarding their driving and crash history, typical workloads, scheduling and payment, trip history over several days, sleep patterns, health, and substance use. All participants will have administered a nasal flow monitor for the detection of obstructive sleep apnoea. Discussion Significant attention has been paid to the enforcement of legislation aiming to deter problems such as excess loading, speeding and substance use; however, there is inconclusive evidence as to the direction and strength of associations of many other postulated risk factors for heavy vehicle crashes. The influence of factors such as remuneration and scheduling on crash risk is unclear; so too the association between sleep apnoea and the risk of heavy vehicle driver crash. Contributory factors such as sleep quality and quantity, body mass and health status will be investigated. Quantifying the measure of effect of these factors on the heavy vehicle driver will inform policy development that aims toward safer driving practices and reduction in heavy vehicle crash; protecting the lives of many on the road network.

XML documents clustering using tensor space model - A preliminary study

A hierarchical structure is used to represent the content of the semi-structured documents such as XML and XHTML. The traditional Vector Space Model (VSM) is not sufficient to represent both the structure and the content of such web documents. Hence in this paper, we introduce a novel method of representing the XML documents in Tensor Space Model (TSM) and then utilize it for clustering. Empirical analysis shows that the proposed method is scalable for a real-life dataset as well as the factorized matrices produced from the proposed method helps to improve the quality of clusters due to the enriched document representation with both the structure and the content information.

Autonomous underwater vehicle trajectory design coupled with predictive ocean models : a case study

Data collection using Autonomous Underwater Vehicles (AUVs) is increasing in importance within the oceano- graphic research community. Contrary to traditional moored or static platforms, mobile sensors require intelligent planning strategies to manoeuvre through the ocean. However, the ability to navigate to high-value locations and collect data with specific scientific merit is worth the planning efforts. In this study, we examine the use of ocean model predictions to determine the locations to be visited by an AUV, and aid in planning the trajectory that the vehicle executes during the sampling mission. The objectives are: a) to provide near-real time, in situ measurements to a large-scale ocean model to increase the skill of future predictions, and b) to utilize ocean model predictions as a component in an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. We present an algorithm designed to generate paths for AUVs to track a dynamically evolving ocean feature utilizing ocean model predictions. This builds on previous work in this area by incorporating the predicted current velocities into the path planning to assist in solving the 3-D motion planning problem of steering an AUV between two selected locations. We present simulation results for tracking a fresh water plume by use of our algorithm. Additionally, we present experimental results from field trials that test the skill of the model used as well as the incorporation of the model predictions into an AUV trajectory planner. These results indicate a modest, but measurable, improvement in surfacing error when the model predictions are incorporated into the planner.

A geometric approach to trajectory design for an autonomous underwater vehicle : surveying the bulbous bow of a ship

In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship for implications of harbor and port security. In recent years, engineers and researchers have been collaborating on automating ship hull inspections by employing autonomous vehicles. Despite the progresses made, human intervention is still necessary at this stage. To increase the functionality of these autonomous systems, we focus on developing model-based control strategies for the survey missions around challenging regions, such as the bulbous bow region of a ship. Recent advances in differential geometry have given rise to the field of geometric control theory. This has proven to be an effective framework for control strategy design for mechanical systems, and has recently been extended to applications for underwater vehicles. Advantages of geometric control theory include the exploitation of symmetries and nonlinearities inherent to the system. Here, we examine the posed inspection problem from a path planning viewpoint, applying recently developed techniques from the field of differential geometric control theory to design the control strategies that steer the vehicle along the prescribed path. Three potential scenarios for surveying a ship?s bulbous bow region are motivated for path planning applications. For each scenario, we compute the control strategy and implement it onto a test-bed vehicle. Experimental results are analyzed and compared with theoretical predictions.