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.

The impact of co-locating regulatory and directional signs on driver performance

The use of intelligent transport systems is proliferating across the Australian road network, particularly on major freeways. New technology allows a greater range of signs and messages to be displayed to drivers. While there has been a long history of human factors analyses of signage, no evaluation has been conducted on this novel, sometimes dynamic, signage or potential interactions when co-located. The purpose of this driving simulator study was to investigate drivers’ behavioural changes and comprehension resulting from the co-location of Lane Use Management Systems with static signs and (Enhanced) Variable Message Signs on Queensland motorways. A section of motorway was simulated, and nine scenarios were developed which presented a combination of signage cases across levels of driving task complexity. Two higher-risk road user groups were targeted for this research on an advanced driving simulator: older (65+ years, N=21) and younger (18-22 years, N=20) drivers. Changes in sign co-location and task complexity had small effect on driver comprehension of the signs and vehicle dynamics variables, including difference with the posted speed limit, headway, standard deviation of lane keeping and brake jerks. However, increasing the amount of information provided to drivers at a given location (by co-locating several signs) increased participants’ gaze duration on the signs. With co-location of signs and without added task complexity, a single gaze was over 2s for more than half of the population tested for both groups, and up to 6 seconds for some individuals.

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.

Not losing the plot : creating, collecting and curating qualitative data through a web-based application

Collecting regular personal reflections from first year teachers in rural and remote schools is challenging as they are busily absorbed in their practice, and separated from each other and the researchers by thousands of kilometres. In response, an innovative web-based solution was designed to both collect data and be a responsive support system for early career teachers as they came to terms with their new professional identities within rural and remote school settings. Using an emailed link to a web-based application named goingok.com, the participants are charting their first year plotlines using a sliding scale from ‘distressed’, ‘ok’ to ‘soaring’ and describing their self-assessment in short descriptive posts. These reflections are visible to the participants as a developing online journal, while the collections of de-identified developing plotlines are visible to the research team, alongside numerical data. This paper explores important aspects of the design process, together with the challenges and opportunities encountered in its implementation. A number of the key considerations for choosing to develop a web application for data collection are initially identified, and the resultant application features and scope are then examined. Examples are then provided about how a responsive software development approach can be part of a supportive feedback loop for participants while being an effective data collection process. Opportunities for further development are also suggested with projected implications for future research.

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.

Fault symptoms of rolling element bearings under variable operating conditions - a multi domain analysis

Diagnostics of rolling element bearings have been traditionally developed for constant operating conditions, and sophisticated techniques, like Spectral Kurtosis or Envelope Analysis, have proven their effectiveness by means of experimental tests, mainly conducted in small-scale laboratory test-rigs. Algorithms have been developed for the digital signal processing of data collected at constant speed and bearing load, with a few exceptions, allowing only small fluctuations of these quantities. Owing to the spreading of condition based maintenance in many industrial fields, in the last years a need for more flexible algorithms emerged, asking for compatibility with highly variable operating conditions, such as acceleration/deceleration transients. This paper analyzes the problems related with significant speed and load variability, discussing in detail the effect that they have on bearing damage symptoms, and propose solutions to adapt existing algorithms to cope with this new challenge. In particular, the paper will i) discuss the implication of variable speed on the applicability of diagnostic techniques, ii) address quantitatively the effects of load on the characteristic frequencies of damaged bearings and iii) finally present a new approach for bearing diagnostics in variable conditions, based on envelope analysis. The research is based on experimental data obtained by using artificially damaged bearings installed on a full scale test-rig, equipped with actual train traction system and reproducing the operation on a real track, including all the environmental noise, owing to track irregularity and electrical disturbances of such a harsh application.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

The IL-6 response to Chlamydia from primary reproductive epithelial cells is highly variable and may be involved in differential susceptibility to the immunopathological consequences of chlamydial infection

Background Chlamydia trachomatis infection results in reproductive damage in some women. The process and factors involved in this immunopathology are not well understood. This study aimed to investigate the role of primary human cellular responses to chlamydial stress response proteases and chlamydial infection to further identify the immune processes involved in serious disease sequelae. Results Laboratory cell cultures and primary human reproductive epithelial cultures produced IL-6 in response to chlamydial stress response proteases (CtHtrA and CtTsp), UV inactivated Chlamydia, and live Chlamydia. The magnitude of the IL-6 response varied considerably (up to 1000 pg ml-1) across different primary human reproductive cultures. Thus different levels of IL-6 production by reproductive epithelia may be a determinant in disease outcome. Interestingly, co-culture models with either THP-1 cells or autologous primary human PBMC generally resulted in increased levels of IL-6, except in the case of live Chlamydia where the level of IL-6 was decreased compared to the epithelial cell culture only, suggesting this pathway may be able to be modulated by live Chlamydia. PBMC responses to the stress response proteases (CtTsp and CtHtrA) did not significantly vary for the different participant cohorts. Therefore, these proteases may possess conserved innate PAMPs. MAP kinases appeared to be involved in this IL-6 induction from human cells. Finally, we also demonstrated that IL-6 was induced by these proteins and Chlamydia from mouse primary reproductive cell cultures (BALB/C mice) and mouse laboratory cell models. Conclusions We have demonstrated that IL-6 may be a key factor for the chlamydial disease outcome in humans, given that primary human reproductive epithelial cell culture showed considerable variation in IL-6 response to Chlamydia or chlamydial proteins, and that the presence of live Chlamydia (but not UV killed) during co-culture resulted in a reduced IL-6 response suggesting this response may be moderated by the presence of the organism.

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 which 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. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Anthropogenic-based regional-scale factors most consistently explain plot-level exotic diversity in grasslands

Aim Evidence linking the accumulation of exotic species to the suppression of native diversity is equivocal, often relying on data from studies that have used different methods. Plot-level studies often attribute inverse relationships between native and exotic diversity to competition, but regional abiotic filters, including anthropogenic influences, can produce similar patterns.We seek to test these alternatives using identical scale-dependent sampling protocols in multiple grasslands on two continents. Location Thirty-two grassland sites in North America and Australia. Methods We use multiscale observational data, collected identically in grain and extent at each site, to test the association of local and regional factors with the plot-level richness and abundance of native and exotic plants. Sites captured environmental and anthropogenic gradients including land-use intensity, human population density, light and soil resources, climate and elevation. Site selection occurred independently of exotic diversity, meaning that the numbers of exotic species varied randomly thereby reducing potential biases if only highly invaded sites were chosen. Results Regional factors associated directly or indirectly with human activity had the strongest associations with plot-level diversity. These regional drivers had divergent effects: urban-based economic activity was associated with high exotic : native diversity ratios; climate- and landscape-based indicators of lower human population density were associated with low exotic : native ratios. Negative correlations between plot-level native and exotic diversity, a potential signature of competitive interactions, were not prevalent; this result did not change along gradients of productivity or heterogeneity. Main conclusion We show that plot-level diversity of native and exotic plants are more consistently associatedwith regional-scale factors relating to urbanization and climate suitability than measures indicative of competition. These findings clarify the long-standing difficulty in resolving drivers of exotic diversity using single-factor mechanisms, suggesting that multiple interacting anthropogenic-based processes best explain the accumulation of exotic diversity in modern landscapes.