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.

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.

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.

Conserved and variable features of gag structure and arrangement in immature retrovirus particles

The assembly of retroviruses is driven by oligomerization of the Gag polyprotein. We have used cryo-electron tomography together with subtomogram averaging to describe the three-dimensional structure of in vitro-assembled Gag particles from human immunodeficiency virus, Mason-Pfizer monkey virus, and Rous sarcoma virus. These represent three different retroviral genera: the lentiviruses, betaretroviruses and alpharetroviruses. Comparison of the three structures reveals the features of the supramolecular organization of Gag that are conserved between genera and therefore reflect general principles of Gag-Gag interactions and the features that are specific to certain genera. All three Gag proteins assemble to form approximately spherical hexameric lattices with irregular defects. In all three genera, the N-terminal domain of CA is arranged in hexameric rings around large holes. Where the rings meet, 2-fold densities, assigned to the C-terminal domain of CA, extend between adjacent rings, and link together at the 6-fold symmetry axis with a density, which extends toward the center of the particle into the nucleic acid layer. Although this general arrangement is conserved, differences can be seen throughout the CA and spacer peptide regions. These differences can be related to sequence differences among the genera. We conclude that the arrangement of the structural domains of CA is well conserved across genera, whereas the relationship between CA, the spacer peptide region, and the nucleic acid is more specific to each genus.

A variable step-size FxLMS algorithm for feedforward active noise control systems based on a new online secondary path modelling technique

Several approaches have been introduced in literature for active noise control (ANC) systems. Since FxLMS algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of FxLMS algorithm. In many ANC applications an online secondary path modelling method using a white noise as a training signal is required to ensure convergence of the system. This paper also proposes a new approach for online secondary path modelling in feedfoward ANC systems. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Benefiting new version of FxLMS algorithm and not continually injection of white noise makes the system more desirable and improves the noise attenuation performance. Comparative simulation results indicate effectiveness of the proposed approach.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Exploring empathy as a variable in the evaluation of professional development programmes for palliative care nurses

Research indicates that empathy, a quality regarded as fundamentally important to nursing practice, is a teachable skill. Because empathic nurse-patient relationships are particularly important in the care of the terminally ill, this has direct relevance to the professional development of palliative care nurses. This article discusses the place of empathy as a criterion variable in the evaluation of a professional development program for palliative care nurses introduced at the Centre for Mental Health Nursing Research at Queensland University of Technology, Brisbane, Australia. A modified version of the Staff-Patient Interaction Response Scale (SPIRS) was used as a pre- and postintervention measure to assess the expressed empathy of the participating nurses. The modifications to SPIR and its coding system to make it suitable for palliative care nursing, and the mechanisms for improving and evaluating the reliability of this instrument will be discussed. The full description of this particular modification of SPIRS for palliative care research is provided as an example of how this instrument could be used in projects for which nurses undertake the difficult task of providing compassionate care to the terminally ill.

A variable diffusivity model for the drying of spherical food particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.