Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Curriculum movements in science education

"The Latin meaning of the word “curriculum” as the race course for athletic sports is a good place to start to describe the use of this word in science education. It conjures up senses of contest and of challenge that have been part of the science curriculum since its earliest beginnings in schooling. Curriculum also had a Latin meaning associating it with the “deeds and events for developing a child to an adult” that also finds resonance in how the teaching and learning of science has in some places and some occasions been conceived. It is this sense of the prescription of an intended curriculum – what is to be taught and learnt in science – that this entry discusses the science curriculum’s movement over time. Others in education, and indeed in science education, use the word “curriculum” much more widely to include the pedagogies in classroom practice, the many other explicit and implicit experiences that ..."--Publisher website

Bikeshare's impact on active travel: Evidence from the United States, Great Britain, and Australia

Over 800 cities globally now offer bikeshare programs. One of their purported benefits is increased physical activity. Implicit in this claim is that bikeshare replaces sedentary modes of transport, particularly car use. This paper estimates the median changes in physical activity levels as a result of bikeshare in the cities of Melbourne, Brisbane, Washington, D.C., London, and Minneapolis/St. Paul. This study is the first known multi-city evaluation of the active travel impacts of bikeshare programs. To perform the analysis, data on mode substitution (i.e. the modes that bikeshare replaces) were used to determine the extent of shift from sedentary to active transport modes (e.g. when a car trip is replaced by bikeshare). Potentially offsetting these gains, reductions in physical activity when walking trips are replaced by bikeshare was also estimated. Finally a Markov Chain Monte Carlo analysis was conducted to estimate confidence bounds on estimated impacts on active travel given uncertainties in data sources. The results indicate that on average 60% of bikeshare trips replace sedentary modes of transport (from 42% in Minneapolis/St. Paul to 67% in Brisbane). When bikeshare replaces a walking trip, there is a reduction in active travel time because walking a given distance takes longer than cycling. Considering the active travel balance sheet for the cities included in this analysis, bikeshare activity in 2012 has an overall positive impact on active travel time. This impact ranges from an additional 1.4 million minutes of active travel for the Minneapolis/St. Paul bikeshare program, to just over 74 million minutes of active travel for the London program The analytical approach adopted to estimate bikeshare’s impact on active travel may act as the basis for future bikeshare evaluations or feasibility studies.

Simulating droplet motion on virtual leaf surfaces

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235–261) with the addition of a disjoining pressure term, describes the gravity- and curvature driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet’s path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.

Theorising South Africa's corporate governance

South Africa’s principal corporate governance report aspires to an ‘inclusive’ approach to corporate governance, in which companies are clearly advised to consider the interests of a variety of stakeholders. Yet, in common with many other countries, there is little discussion of the theoretical foundations and assumptions implicit in the recommended approach to corporate governance. The purpose of this article is to provide an analysis of corporate governance and the corporate environment in South Africa in terms of existing theory and models of corporate governance, and to provide a critique based on a consideration of traditional African values and the socio-economic necessities of post-apartheid South Africa. The result is the identification of an incompatibility between the current corporate environment in South Africa and the given exposition of African values. Some prospects for change are then identified.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Revisiting the Australian code of banking practice: Is self-regulation still relevant for improving consumer protection standards?

The Code of Banking Practice is one of the oldest examples of consumer protection provided through self-regulation in the Australian financial services sector. However, since the Banking Code was first released in 1993, the volume of consumer protection legislation applying to banks has increased exponentially and parts of the Banking Code that once provided new consumer rights have now been largely superseded by legislation. In light of the increasingly complex set of laws and regulations that govern the relationship between banks and their consumer and small business customers it could be argued that the Banking Code has a limited future role. However, an analysis of the Banking Code shows that it adds to the consumer protection standards provided by legislation and can continue to facilitate improvements in the standards of subscribing banks and of other institutions in the financial services sector. Self-regulation and industry codes should continue to be part of the regulatory mix. Any regulatory changes that flow from the recent Financial System Inquiry should also facilitate and support the self-regulation role, but the government should also consider further changes to encourage improvements in industry codes and ensure that the implicit regulatory benefits that are provided, in part, because of the existence of industry codes, are made explicit and made available only to code subscribers.

A finite element modelling method for thin layer mortared masonry systems

This paper deals with a finite element modelling method for thin layer mortared masonry systems. In this method, the mortar layers including the interfaces are represented using a zero thickness interface element and the masonry units are modelled using an elasto-plastic, damaging solid element. The interface element is formulated using two regimes; i) shear-tension and ii) shearcompression. In the shear-tension regime, the failure of joint is consiedered through an eliptical failure criteria and in shear-compression it is considered through Mohr Coulomb type failure criterion. An explicit integration scheme is used in an implicit finite element framework for the formulation of the interface element. The model is calibrated with an experimental dataset from thin layer mortared masonry prism subjected to uniaxial compression, a triplet subjected to shear loads a beam subjected to flexural loads and used to predict the response of thin layer mortared masonry wallettes under orthotropic loading. The model is found to simulate the behaviour of a thin layer mortated masonry shear wall tested under pre-compression and inplane shear quite adequately. The model is shown to reproduce the failure of masonry panels under uniform biaxial state of stresses.

Putting an "end" to the motor cortex representations of action words

Language processing is an example of implicit learning of multiple statistical cues that provide probabilistic information regarding word structure and use. Much of the current debate about language embodiment is devoted to how action words are represented in the brain, with motor cortex activity evoked by these words assumed to selectively reflect conceptual content and/or its simulation. We investigated whether motor cortex activity evoked by manual action words (e.g., caress) might reflect sensitivity to probabilistic orthographic-phonological cues to grammatical category embedded within individual words. We first review neuroimaging data demonstrating that nonwords evoke activity much more reliably than action words along the entire motor strip, encompassing regions proposed to be action category specific. Using fMRI, we found that disyllabic words denoting manual actions evoked increased motor cortex activity compared with non-body-part-related words (e.g., canyon), activity which overlaps that evoked by observing and executing hand movements. This result is typically interpreted in support of language embodiment. Crucially, we also found that disyllabic nonwords containing endings with probabilistic cues predictive of verb status (e.g., -eve) evoked increased activity compared with nonwords with endings predictive of noun status (e.g., -age) in the identical motor area. Thus, motor cortex responses to action words cannot be assumed to selectively reflect conceptual content and/or its simulation. Our results clearly demonstrate motor cortex activity reflects implicit processing of ortho-phonological statistical regularities that help to distinguish a word's grammatical class.

Direct mapping of hippocampal surfaces with intrinsic shape context

We propose in this paper a new method for the mapping of hippocampal (HC) surfaces to establish correspondences between points on HC surfaces and enable localized HC shape analysis. A novel geometric feature, the intrinsic shape context, is defined to capture the global characteristics of the HC shapes. Based on this intrinsic feature, an automatic algorithm is developed to detect a set of landmark curves that are stable across population. The direct map between a source and target HC surface is then solved as the minimizer of a harmonic energy function defined on the source surface with landmark constraints. For numerical solutions, we compute the map with the approach of solving partial differential equations on implicit surfaces. The direct mapping method has the following properties: (1) it has the advantage of being automatic; (2) it is invariant to the pose of HC shapes. In our experiments, we apply the direct mapping method to study temporal changes of HC asymmetry in Alzheimer's disease (AD) using HC surfaces from 12 AD patients and 14 normal controls. Our results show that the AD group has a different trend in temporal changes of HC asymmetry than the group of normal controls. We also demonstrate the flexibility of the direct mapping method by applying it to construct spherical maps of HC surfaces. Spherical harmonics (SPHARM) analysis is then applied and it confirms our results on temporal changes of HC asymmetry in AD.

Non-parametric consistency test for multiple-sensing-modality data fusion

Fusing data from multiple sensing modalities, e.g. laser and radar, is a promising approach to achieve resilient perception in challenging environmental conditions. However, this may lead to \emph{catastrophic fusion} in the presence of inconsistent data, i.e. when the sensors do not detect the same target due to distinct attenuation properties. It is often difficult to discriminate consistent from inconsistent data across sensing modalities using local spatial information alone. In this paper we present a novel consistency test based on the log marginal likelihood of a Gaussian process model that evaluates data from range sensors in a relative manner. A new data point is deemed to be consistent if the model statistically improves as a result of its fusion. This approach avoids the need for absolute spatial distance threshold parameters as required by previous work. We report results from object reconstruction with both synthetic and experimental data that demonstrate an improvement in reconstruction quality, particularly in cases where data points are inconsistent yet spatially proximal.

Can’t see the trees for the forest? Why IS-ServQual items matter

Despite longstanding concern with the dimensionality of the service quality construct as measured by ServQual and IS-ServQual instruments, variations on the IS-ServQual instrument have been enduringly prominent in both academic research and practice in the field of IS. We explain the continuing popularity of the instrument based on the salience of the item set for predicting overall customer satisfaction, suggesting that the preoccupation with the dimensions has been a distraction. The implicit mutual exclusivity of the items suggests a more appropriate conceptualization of IS-ServQual as a formative index. This conceptualization resolves the paradox in IS-ServQual research, that of how an instrument with such well-known and well-documented weaknesses continue to be very influential and widely used by academics and practitioners. A formative conceptualization acknowledges and addresses the criticisms of IS-ServQual, while simultaneously explaining its enduring salience by focusing on the items rather than the “dimensions.” By employing an opportunistic sample and adopting the most recent IS-ServQual instrument published in a leading IS journal (virtually, any valid IS- ServQual sample in combination with a previously tested instrument variant would suffice for study purposes), we demonstrate that when re-specified as both first-order and second-order formatives, IS-ServQual has good model quality metrics and high predictive power on customer satisfaction. We conclude that this formative specification has higher practical use and is more defensible theoretically.

The role of time pressure and different psychological safety climate referents in the prediction of nurses’ hand hygiene compliance

In this study of 638 Australian nurses, compliance to hand hygiene (HH), as defined by the “five moments” recommended by the World Health Organisation (2009), was examined. Hypotheses focused on the extent to which time pressure reduces compliance and safety climate (operationalised in relation to HH using colleagues, manager, and hospital as referents) increases compliance. It also was proposed that HH climate would interact with time pressure, such that the negative effects of time pressure would be less marked when HH climate is high. The extent to which the three HH climate variables would interact among each other, either in the form of boosting or compensatory effects, was tested in an exploratory manner. A prospective research design was used in which time pressure and the HH climate variables were assessed at Time 1 and compliance was assessed by self-report two weeks later. Compliance was high but varied significantly across the 5 HH Moments, suggesting that nurses make distinctions between inherent and elective HH and also seemed to engage in some implicit rationing of HH. Time pressure dominated the utility of HH climate to have its positive impact on compliance. The most conducive workplace for compliance was one low in time pressure and high in HH climate. Colleagues were very influential in determining compliance, more so than the manager and hospital. Manager and hospital support for HH enhanced the positive effects of colleagues on compliance. Providing training and enhancing knowledge was important, not just for compliance, but for safety climate.