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.

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.

Effects of speeding and headway related variable message signs on driver behaviour and attitudes

This research project examined objective measures of driver behaviour and road users' perceptions on the usefulness and effectiveness of three specific VMS (Variable Message Signs) interventions to improve speeding and headway behaviours. The interventions addressed speeding behaviour alone (intervention 1), headway behaviour alone (intervention 2) and a combination of speeding and headway behaviour (intervention 3). Six VMS were installed along a segment of the Bruce Highway, with a series of three signs for each of the northbound and southbound traffic. Speeds and headway distances were measured with loop detectors installed before and after each VMS. Messages addressing speeding and headway were devised for display on the VMS. A driver could receive a message if they were detected as exceeding the posted speed limit (of 90km/hr) or if the distance to the vehicle in front was less than 2.0s. In addition to the on-road objective measurement of speeding and headway behaviours, the research project elicited self-reported responses to the speeding and headway messages from a sample of drivers via a community-based survey. The survey sought to examine the drivers' beliefs about the effectiveness of the signs and messages, and their views about the role, use, and effectiveness of VMS more generally.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

BRCA1 is an essential mediator of vinorelbine-induced apoptosis in mesothelioma

The rapeutic options for malignant pleural mesothelioma (MPM) are limited despite the increasing incidence globally. The vinca alkaloid vinorelbine exhibits clinical activity; however, to date, treatment optimization has not been achieved using biomarkers. BRCA1 regulates sensitivity to microtubule poisons; however, its role in regulating vinorelbine-induced apoptosis in mesothelioma is unknown. Here we demonstrate that BRCA1 plays an essential role in mediating vinorelbine-induced apoptosis, as evidenced by (1) the strong correlation between vinorelbine sensitivity and BRCA1 expression level; (2) induction of resistance to vinorelbine by BRCA1 using siRNA oligonucleotides; (3) dramatic down-regulation of BRCA1 following selection for vinorelbine resistance; and (4) the re-activation of vinorelbine-induced apoptosis following re-expression of BRCA1 in resistant cells. To determine whether loss of BRCA1 expression in mesothelioma was potentially relevant in vivo, BRCA1 immunohistochemistry was subsequently performed on 144 primary mesothelioma specimens. Loss of BRCA1 protein expression was identified in 38.9% of samples. Together, these data suggest that BRCA1 plays a critical role in mediating apoptosis by vinorelbine in mesothelioma, warranting its clinical evaluation as a predictive biomarker. Copyright © 2012 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.

Multiphysics modelling of convective drying of food materials

Currently, 1.3 billion tonnes of food is lost annually due to lack of proper processing and preservation method. Drying is one of the easiest and oldest methods of food processing which can contribute to reduce that huge losses, combat hunger and promote food security. Drying increase shelf life, reduce weight and volume of food thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. However, drying is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the food material. Modelling of this process is essential to optimize the drying kinetics and improve energy efficiency of the process. Since material properties varies with moisture content, the models should not consider constant materials properties, constant diffusion .The objective of this paper is to develop a multiphysics based mathematical model to simulate coupled heat and mass transfer during convective drying of fruit considering variable material properties. This model can be used predict the temperature and moisture distribution inside the food during drying. Effect of different drying air temperature and drying air velocity on drying kinetics has been demonstrated. The governing equations of heat and mass transfer were solved with Comsol Multiphysics 4.3.

Essential elements for recruitment and retention : Generation Y

Purpose: Generation Y (Gen Y) is the newest and largest generation entering the workforce. Gen Y may differ from previous generations in work-related characteristics which may have recruitment and retention repercussions. Currently, limited theoretically-based research exists regarding Gen Y’s work expectations and goals in relation to undergraduate students and graduates. Design/methodology/approach: This study conducted a theoretically-based investigation of the work expectations and goals of student- and working-Gen Y individuals based within a framework incorporating both expectancy-value and goal setting theories. N = 398 provided useable data via an on-line survey. Findings: Overall, some support was found for predictions with career goals loading on a separate component to daily work expectations and significant differences between student- and working- Gen Y on career goals. No significant differences were found, however, between the two groups in daily work expectations. Research limitations/implications: Future research may benefit from adopting a theoretical framework which assesses both daily work expectations and career goals when examining the factors which motivate Gen Y’s decisions to join and remain at a particular organisation. Practical implications: At a practical level, based on the findings, some examples are provided of the means by which organisations may draw upon daily work expectations and career goals of importance to Gen Y and, in doing so, influence the likelihood that a Gen Y individual will join and remain at their particular organisation. Originality/value: This research has demonstrated the utility of adopting a sound theoretical framework in furthering understanding about the motivations which influence organisations’ ability to recruit and retain Gen Y, among both student Gen Y as well as those Gen Y individuals who are already working.

Assessing performance and capability in the work place : focusing on essential skills and knowledge in student work placements

The determination of performance standards and assessment practices in regard to student work placements is an essential and important task. Inappropriate, inadequate, or excessively complex assessment tasks can influence levels of student engagement and the quality of learning outcomes. Critical to determining appropriate standards and assessment tasks is an understanding and knowledge of key elements of the learning environment and the extent to which opportunities are provided for students to engage in critical reflection and judgement of their own performance in the contexts of the work environment. This paper focuses on the development of essential skills and knowledge (capabilities) that provide evidence of learning in work placements by describing an approach taken in the science and technology disciplines. Assessment matrices are presented to illustrate a method of assessment for use within the context of the learning environment centred on work placements in science and technology. This study contributes to the debate on the meaning of professional capability, performance standards and assessment practices in work placement programs by providing evidence of an approach that can be adapted by other programs to achieve similar benefits. The approach may also be valuable to other learning contexts where capability and performance are being judged in situations that are outside a controlled teaching and learning environment i.e. in other life-wide learning contexts.

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.

Income Tax : Text, Materials and Essential Cases [8th ed.]

Tax law and policy is a vital part of Australian society. Australian society insists that the Federal Government provide extensive public programs, such as health services, education, social security, foreign aid, legal infra¬structure, regulation, police services, national defence and funding for sports development. These programs are costly to provide and are funded by taxation. The aim of this book is to introduce and explain the principles of tax law and tax policy in plain English. The book contains detailed commentary on tax principles together with extracts from cases and materials that illustrate the application of the principles. The book considers tax policy and the economic and social aspects of tax law. While tax students must develop technical competence in tax law, given the speed with which changes are made to the technical details of tax law, it is also important to grasp tax principles and policy to understand why tax law has changed or why it should change. The chapters are structured to direct readers to the key provisions of the tax law. Each case is introduced by an explanation of the facts, followed by the taxpayer’s arguments, the Commissioner’s assertions and the decision of the Administrative Appeals Tribunal or a court. The commentary guides readers through the issues considered in the judgments. The book contains extracts from: articles; materials dealing with tax policy; and the Commissioner’s rulings. The book also has references for further reading and medium-neutral citations (Internet citations) for cases decided since 1998.

Using variable speed limits for motorway off-ramp queue protection

Motorway off-ramps are a significant source of traffic congestion and collisions. Heavy diverging traffic to off-ramps slows down the mainline traffic speed. When the off-ramp queue spillbacks onto the mainline, it leads to a major breakdown of the motorway capacity and a significant threat to the traffic safety. This paper proposes using Variable Speed Limits (VSL) for protection of the motorway off-ramp queue and thus to promote safety in congested diverging areas. To support timely activation of VSL in advance of queue spillover, a proactive control strategy is proposed based on a real-time off-ramp queue estimation and prediction. This process determines the estimated queue size in the near-term future, on which the decision to change speed limits is made. VSL can effectively slow down traffic as it is mandatory that drivers follow the changed speed limits. A collateral benefit of VSL is its potential effect on drivers making them more attentive to the surrounding traffic conditions, and prepared for a sudden braking of the leading car. This paper analyses and quantifies these impacts and potential benefits of VSL on traffic safety and efficiency using the microsimulation approach.