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.

Estimating the robustness of long-haul train plans

In Australia, and elsewhere, the movement of trains on long-haul rail networks is usually planned in advance. Typically, a train plan is developed to confirm that the required train movements and track maintenance activities can occur. The plan specifies when track segments will be occupied by particular trains and maintenance activities. On the day of operation, a train controller monitors and controls the movement of trains and maintenance crews, and updates the train plan in response to unplanned disruptions. It can be difficult to predict how good a plan will be in practice. The main performance indicator for a train service should be reliability - the proportion of trains running the service that complete at or before the scheduled time. We define the robustness of a planned train service to be the expected reliability. The robustness of individual train services and for a train plan as a whole can be estimated by simulating the train plan many times with random, but realistic, perturbations to train departure times and segment durations, and then analysing the distributions of arrival times. This process can also be used to set arrival times that will achieve a desired level of robustness for each train service.

ACE research vignette 028 : Does it pay for established firms to be entrepreneurial?

This series of research vignettes is aimed at sharing current and interesting research findings from our team of international Entrepreneurship researchers. This vignette, written by Professor Per Davidsson, examines the evidence on the effects of a firm’s level of “entrepreneurial orientation” on business performance, across different contexts.

The effect of organ motion of radiotherapy plans

Organ motion as a result of respiration is an important field of research for medical physics. Knowledge of magnitude and direction of this motion is necessary to allow for more accurate radiotherapy treatment planning. This will result in higher doses to the tumour whilst sparing healthy tissue. This project involved human trials, where the radiation therapy patient's kidneys were CT scanned under three different conditions; whilst free breathing (FB), breath-hold at normal tidal inspiration (BHIN), and breath-hold at normal tidal expiration (BHEX). The magnitude of motion was measured by recording the outline of the kidney from a Beam's Eye View (BEV). The centre of mass of this 2D shape was calculated for each set using "ImageJ" software and the magnitude of movement determined from the change in the centroid's coordinates between the BHIN and BHEX scans. The movement ranged from, for the left and right kidneys, 4-46mm and 2-44mm in the superior/inferior (axial) plane, 1-21mm and 2- 16mm in the anterior/posterior (coronal) plane, and 0-6mm and 0-8mm in the lateral/medial (sagittal) plane. From exhale to inhale, the kidneys tended to move inferiorly, anteriorly and laterally. A standard radiotherapy plan, designed to treat the para-aortics with opposed lateral fields was performed on the free breathing (planning) CT set. The field size and arrangement was set up using the same parameters for each subject. The prescription was to deliver 45 Gray in 25 fractions. This field arrangement and prescription was then copied over to the breath hold CT sets, and the dosimetric differences were compared using Dose Volume Histograms (DVH). The point of comparison for the three sets was recorded as the percentage volume of kidney receiving less than or equal to 10 Gray. The QUASAR respiratory motion phantom was used with the range of motion determined from the human study. The phantom was imaged, planned and treated with a linear accelerator with dose determined by film. The effect of the motion was measured by the change in the penumbra of the film and compared to the penumbra from the treatment planning system.

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.

A new procedure for using envelope analysis for rolling element bearing diagnostics in variable operating conditions

In the field of rolling element bearing diagnostics envelope analysis, and in particular the squared envelope spectrum, have gained in the last years a leading role among the different digital signal processing techniques. The original constraint of constant operating speed has been relaxed thanks to the combination of this technique with the computed order tracking, able to resample signals at constant angular increments. In this way, the field of application of squared envelope spectrum has been extended to cases in which small speed fluctuations occur, maintaining the effectiveness and efficiency that characterize this successful technique. However, the constraint on speed has to be removed completely, making envelope analysis suitable also for speed and load transients, to implement an algorithm valid for all the industrial application. In fact, in many applications, the coincidence of high bearing loads, and therefore high diagnostic capability, with acceleration-deceleration phases represents a further incentive in this direction. This paper is aimed at providing and testing a procedure for the application of envelope analysis to speed transients. The effect of load variation on the proposed technique will be also qualitatively addressed.

Application of cepstrum pre-whitening for the diagnosis of bearing faults under variable speed conditions

Diagnostics of rolling element bearings involves a combination of different techniques of signal enhancing and analysis. The most common procedure presents a first step of order tracking and synchronous averaging, able to remove the undesired components, synchronous with the shaft harmonics, from the signal, and a final step of envelope analysis to obtain the squared envelope spectrum. This indicator has been studied thoroughly, and statistically based criteria have been obtained, in order to identify damaged bearings. The statistical thresholds are valid only if all the deterministic components in the signal have been removed. Unfortunately, in various industrial applications, characterized by heterogeneous vibration sources, the first step of synchronous averaging is not sufficient to eliminate completely the deterministic components and an additional step of pre-whitening is needed before the envelope analysis. Different techniques have been proposed in the past with this aim: The most widely spread are linear prediction filters and spectral kurtosis. Recently, a new technique for pre-whitening has been proposed, based on cepstral analysis: the so-called cepstrum pre-whitening. Owing to its low computational requirements and its simplicity, it seems a good candidate to perform the intermediate pre-whitening step in an automatic damage recognition algorithm. In this paper, the effectiveness of the new technique will be tested on the data measured on a full-scale industrial bearing test-rig, able to reproduce the harsh conditions of operation. A benchmark comparison with the traditional pre-whitening techniques will be made, as a final step for the verification of the potentiality of the cepstrum pre-whitening.