Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

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.

Loss to assets : production of power from speed breaker

In this work, prospect and feasibility of power generation by using speed breakers has been investigated. In this project a mechanism to generate power by converting the potential energy generated by a vehicle going up on a speed breaker into kinetic energy. This arrangement is made one rotation as soon as the vehicle moves over the speed breaker and has been increased using gears. After the production electricity, a storing unit has been used to hoard the generated electricity during the day and will be used during the night. Two prototypes have made using rack and pinion gear, spur gear, springs and generator .From which a considerable amount of energy is obtained. Nonetheless the cost of the prototype was inexpensive which proves the feasibility of this project and the idea can be applied on heavy traffic roads. Further investigation is being carried on to introduce the technology for practical approach.

Developing guidelines for intervention to reduce risk of low-speed vehicle run-overs of young children

In Australia, research suggests that up to one quarter of child pedestrian hospitalisations result from driveway run-over incidents (Pinkney et al., 2006). In Queensland, these numbers equate to an average of four child fatalities and 81 children presenting at hospital emergency departments every year (The Commission for Children, Young People and Child Guardian). National comparison shows that these numbers represent a slightly higher per capita rate (23.5% of all deaths). To address this issue, the current research was undertaken with the aim to develop an educative intervention based on data collected from parents and caregivers of young children. Thus, the current project did not seek to use available intervention or educational material, but to develop a new evidence-based intervention specifically targeting driveway run-overs involving young children. To this end, general behavioural and environmental changes that caregivers had undertaken in order to reduce the risk of injury to any child in their care were investigated. Broadly, the first part of this report sought to: • develop a conceptual model of established domestic safety behaviours, and to investigate whether this model could be successfully applied to the driveway setting; • explore and compare sources of knowledge regarding domestic and driveway child safety; and • examine the theoretical implications of current domestic and driveway related behaviour and knowledge among caregivers. The aim of the second part of this research was to develop and test the efficacy of an intervention based on the findings in the first part of the research project. Specifically, it sought to: • develop an educational driveway intervention that is based on current safety behaviours in the domestic setting and informed by existing knowledge of driveway safety and behaviour change theory; and • evaluate its efficacy in a sample of parents and caregivers.

Point-to-point speed enforcement

This report reviews the use of point-to-point speed enforcement internationally in order to provide principles for better practice for its use in Australia and New Zealand. Point-to-point enforcement is a relatively new technological approach to speed enforcement which involves measuring the average speed of vehicles passing a series of cameras, by using automatic number plate recognition (ANPR) and other technologies. The approach has been implemented or trialled in a number of countries including Australia, New Zealand, the United Kingdom, the Netherlands, Austria, Italy, Switzerland and France. The major research activities were undertaken for the preparation of this report included: (1) an extensive review of the international literature; (2) stakeholder consultation with international and domestic organisations. To date, there have been no formal evaluations of point-to- point speed enforcement in Australia or New Zealand.

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.

Beyond barcoding : a mitochondrial genomics approach to molecular phylogenetics and diagnostics of blowflies (Diptera: Calliphoridae)

Members of the Calliphoridae (blowflies) are significant for medical and veterinary management, due to the ability of some species to consume living flesh as larvae, and for forensic investigations due to the ability of others to develop in corpses. Due to the difficulty of accurately identifying larval blowflies to species there is a need for DNA-based diagnostics for this family, however the widely used DNA-barcoding marker, cox1, has been shown to fail for several groups within this family. Additionally, many phylogenetic relationships within the Calliphoridae are still unresolved, particularly deeper level relationships. Sequencing whole mt genomes has been demonstrated both as an effective method for identifying the most informative diagnostic markers and for resolving phylogenetic relationships. Twenty-seven complete, or nearly so, mt genomes were sequenced representing 13 species, seven genera and four calliphorid subfamilies and a member of the related family Tachinidae. PCR and sequencing primers developed for sequencing one calliphorid species could be reused to sequence related species within the same superfamily with success rates ranging from 61% to 100%, demonstrating the speed and efficiency with which an mt genome dataset can be assembled. Comparison of molecular divergences for each of the 13 protein-coding genes and 2 ribosomal RNA genes, at a range of taxonomic scales identified novel targets for developing as diagnostic markers which were 117–200% more variable than the markers which have been used previously in calliphorids. Phylogenetic analysis of whole mt genome sequences resulted in much stronger support for family and subfamily-level relationships. The Calliphoridae are polyphyletic, with the Polleninae more closely related to the Tachinidae, and the Sarcophagidae are the sister group of the remaining calliphorids. Within the Calliphoridae, there was strong support for the monophyly of the Chrysomyinae and Luciliinae and for the sister-grouping of Luciliinae with Calliphorinae. Relationships within Chrysomya were not well resolved. Whole mt genome data, supported the previously demonstrated paraphyly of Lucilia cuprina with respect to L. sericata and allowed us to conclude that it is due to hybrid introgression prior to the last common ancestor of modern sericata populations, rather than due to recent hybridisation, nuclear pseudogenes or incomplete lineage sorting.

A practical signal processing approach for condition monitoring of low speed machinery using Peak-Hold-Down-Sample algorithm

A simple and effective down-sample algorithm, Peak-Hold-Down-Sample (PHDS) algorithm is developed in this paper to enable a rapid and efficient data transfer in remote condition monitoring applications. The algorithm is particularly useful for high frequency Condition Monitoring (CM) techniques, and for low speed machine applications since the combination of the high sampling frequency and low rotating speed will generally lead to large unwieldy data size. The effectiveness of the algorithm was evaluated and tested on four sets of data in the study. One set of the data was extracted from the condition monitoring signal of a practical industry application. Another set of data was acquired from a low speed machine test rig in the laboratory. The other two sets of data were computer simulated bearing defect signals having either a single or multiple bearing defects. The results disclose that the PHDS algorithm can substantially reduce the size of data while preserving the critical bearing defect information for all the data sets used in this work even when a large down-sample ratio was used (i.e., 500 times down-sampled). In contrast, the down-sample process using existing normal down-sample technique in signal processing eliminates the useful and critical information such as bearing defect frequencies in a signal when the same down-sample ratio was employed. Noise and artificial frequency components were also induced by the normal down-sample technique, thus limits its usefulness for machine condition monitoring applications.

Automated speed enforcement in Australia : recent examples of the influence of public opinion on program sustainability

In Australia, speeding remains a substantial contributor to road trauma. The National Road Safety Strategy (2011-2020) highlighted the need to harness community support for current and future speed management strategies. Australia is known for intensive speed camera programs which are both automated and manual, employing covert and overt methods. Recent developments in the area of automated speed enforcement in Australia help to illustrate the important link between community attitudes to speed enforcement and subsequent speed camera policy developments. A perceived lack of community confidence in camera programs prompted reviews in New South Wales and Victoria in 2011 by the jurisdictional Auditor-General. This paper explores automated speed camera enforcement in Australia with particular reference to the findings of these two reports as they relate to the level of public support for and community attitudes towards automated speed enforcement. It also provides comment on the evolving nature of automated speed enforcement according to previously identified controversies and dilemmas associated with speed camera programs.

Speed enforcement in China : national, provincial and city initiatives and their success

China is motorizing rapidly, with associated urban road development and extensive construction of motorways. Speeding accounts for about 10% of fatalities, which represents a large decrease from a peak of 17.2% in 2004. Speeding has been addressed at a national level through the introduction of laws and procedural requirements in 2004, in provinces either across all road types or on motorways, and at city level. Typically, documentation of speed enforcement programmes has taken place when new technology (i.e. speed cameras) is introduced, and it is likely that many programmes have not been documented or widely reported. In particular, the national legislation of 2004 and its implementation was associated with a large reduction in fatalities attributed to speeding. In Guangdong Province, after using speed detection equipment, motorway fatalities due to speeding in 2005 decreased by 32.5% comparing with 2004. In Beijing, the number of traffic monitoring units which were used to photograph illegal traffic activities such as traffic light violations, speeding and using bus lanes illegally increased to 1958 by April 1, 2009, and in the future such automated enforcement will become the main means of enforcement, expected to account for 60% of all traffic enforcement in Beijing. This paper provides a brief overview of the speeding enforcement programmes in China which have been documented and their successes.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Effects of average speed enforcement on speed compliance and crashes : a review of the literature

Average speed enforcement is a relatively new approach gaining popularity throughout Europe and Australia. This paper reviews the evidence regarding the impact of this approach on vehicle speeds, crashes rates and a number of additional road safety and public health outcomes. The economic and practical viability of the approach as a road safety countermeasure is also explored. A literature review, with an international scope, of both published and grey literature was conducted. There is a growing body of evidence to suggest a number of road safety benefits associated with average speed enforcement, including high rates of compliance with speed limits, reductions in average and 85th percentile speeds and reduced speed variability between vehicles. Moreover, the approach has been demonstrated to be particularly effective in reducing excessive speeding behaviour. Reductions in crash rates have also been reported in association with average speed enforcement, particularly in relation to fatal and serious injury crashes. In addition, the approach has been shown to improve traffic flow, reduce vehicle emissions and has also been associated with high levels of public acceptance. Average speed enforcement offers a greater network-wide approach to managing speeds that reduces the impact of time and distance halo effects associated with other automated speed enforcement approaches. Although comparatively expensive it represents a highly reliable approach to speed enforcement that produces considerable returns on investment through reduced social and economic costs associated with crashes.