Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/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 a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Spatially explicit structural equation modeling

Structural equation modeling (SEM) is a powerful statistical approach for the testing of networks of direct and indirect theoretical causal relationships in complex data sets with intercorrelated dependent and independent variables. SEM is commonly applied in ecology, but the spatial information commonly found in ecological data remains difficult to model in a SEM framework. Here we propose a simple method for spatially explicit SEM (SE-SEM) based on the analysis of variance/covariance matrices calculated across a range of lag distances. This method provides readily interpretable plots of the change in path coefficients across scale and can be implemented using any standard SEM software package. We demonstrate the application of this method using three studies examining the relationships between environmental factors, plant community structure, nitrogen fixation, and plant competition. By design, these data sets had a spatial component, but were previously analyzed using standard SEM models. Using these data sets, we demonstrate the application of SE-SEM to regularly spaced, irregularly spaced, and ad hoc spatial sampling designs and discuss the increased inferential capability of this approach compared with standard SEM. We provide an R package, sesem, to easily implement spatial structural equation modeling.

Electrochemical mechanism of eugenol at a Cu doped gold nanoparticles modified glassy carbon electrode and its analytical application in food samples

A simple one-step electrodeposition method was used to construct a glassy carbon electrode (GCE), which has been modified with Cu doped gold nanoparticles (GNPs), i.e. a Cu@AuNPs/GCE. This electrode was characterized with the use of scanning electron microscopy (SEM) and X-ray diffraction (XRD) techniques. The eugenol was electrocatalytically oxidized at the Cu@AuNPs/GCE. At this electrode, in comparison with the behavior at the GCE alone, the corresponding oxidation peak current was enhanced and the shift of the oxidation potentials to lower values was observed. Electrochemical behavior of eugenol at the Cu@AuNPs/GCE was investigated with the use of the cyclic voltammetry (CV) technique, and additionally, in order to confirm the electrochemical reaction mechanism for o-methoxy phenols, CVs for catechol, guaiacol and vanillin were investigated consecutively. Based on this work, an electrochemical reaction mechanism for o-methoxy phenols was suggested, and in addition, the above Cu@AuNPs/GCE was successfully employed for the analysis of eugenol in food samples.

Critical reflection: Part of everyday practices

Critical reflection is central to improving practices in early years services. It is also a learned skill.

Assessment of body composition in Sri Lankan children: Validation of a bioelectrical impedance prediction equation

Objective: To develop bioelectrical impedance analysis (BIA) equations to predict total body water (TBW) and fat-free mass (FFM) of Sri Lankan children. Subjects/Methods: Data were collected from 5- to 15-year-old healthy children. They were randomly assigned to validation (M/F: 105/83) and cross-validation (M/F: 53/41) groups. Height, weight and BIA were measured. TBW was assessed using isotope dilution method (D2 O). Multiple regression analysis was used to develop preliminary equations and cross-validated on an independent group. Final prediction equation was constructed combining the two groups and validated by PRESS (prediction of sum of squares) statistics. Impedance index (height2/impedance; cm2/Ω), weight and sex code (male = 1; female = 0) were used as variables. Results: Independent variables of the final prediction equation for TBW were able to predict 86.3% of variance with root means-squared error (RMSE) of 2.1l. PRESS statistics was 2.1l with press residuals of 1.2l. Independent variables were able to predict 86.9% of variance of FFM with RMSE of 2.7 kg. PRESS statistics was 2.8 kg with press residuals of 1.4 kg. Bland Altman technique showed that the majority of the residuals were within mean bias±1.96 s.d. Conclusions: Results of this study provide BIA equation for the prediction of TBW and FFM in Sri Lankan children. To the best of our knowledge there are no published BIA prediction equations validated on South Asian populations. Results of this study need to be affirmed by more studies on other closely related populations by using multi-component body composition assessment.

Path algebra for mobile robots

In this paper, we introduce a path algebra well suited for navigation in environments that can be abstracted as topological graphs. From this path algebra, we derive algorithms to reduce routes in such environments. The routes are reduced in the sense that they are shorter (contain fewer edges), but still connect the endpoints of the initial routes. Contrary to planning methods descended from Disjktra’s Shortest Path Algorithm like D , the navigation methods derived from our path algebra do not require any graph representation. We prove that the reduced routes are optimal when the graphs are without cycles. In the case of graphs with cycles, we prove that whatever the length of the initial route, the length of the reduced route is bounded by a constant that only depends on the structure of the environment.

Modified Stranski–Krastanov growth in Ge/Si heterostructures via nanostenciled pulsed laser deposition

The combination of nanostenciling with pulsed laser deposition (PLD) provides a flexible, fast approach for patterning the growth of Ge on Si. Within each stencilled site, the morphological evolution of the Ge structures with deposition follows a modified Stranski–Krastanov (SK) growth mode. By systematically varying the PLD parameters (laser repetition rate and number of pulses) on two different substrate orientations (111 and 100), we have observed corresponding changes in growth morphology, strain and elemental composition using scanning electron microscopy, atomic force microscopy and μ-Raman spectroscopy. The growth behaviour is well predicted within a classical SK scheme, although the Si(100) growth exhibits significant relaxation and ripening with increasing coverage. Other novel aspects of the growth include the increased thickness of the wetting layer and the kinetic control of Si/Ge intermixing via the PLD repetition rate.

MRI-based strain and strain rate analysis of left ventricle: A modified hierarchical transformation model

Background Different from other indicators of cardiac function, such as ejection fraction and transmitral early diastolic velocity, myocardial strain is promising to capture subtle alterations that result from early diseases of the myocardium. In order to extract the left ventricle (LV) myocardial strain and strain rate from cardiac cine-MRI, a modified hierarchical transformation model was proposed. Methods A hierarchical transformation model including the global and local LV deformations was employed to analyze the strain and strain rate of the left ventricle by cine-MRI image registration. The endocardial and epicardial contour information was introduced to enhance the registration accuracy by combining the original hierarchical algorithm with an Iterative Closest Points using Invariant Features algorithm. The hierarchical model was validated by a normal volunteer first and then applied to two clinical cases (i.e., the normal volunteer and a diabetic patient) to evaluate their respective function. Results Based on the two clinical cases, by comparing the displacement fields of two selected landmarks in the normal volunteer, the proposed method showed a better performance than the original or unmodified model. Meanwhile, the comparison of the radial strain between the volunteer and patient demonstrated their apparent functional difference. Conclusions The present method could be used to estimate the LV myocardial strain and strain rate during a cardiac cycle and thus to quantify the analysis of the LV motion function.

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "Working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.

Fatigue capacity of cold-formed steel roof battens under cyclic wind uplift loads

Steel roofs made of thin cold-formed steel roof claddings and battens are widely used in low-rise residential and industrial buildings all around the world. However, they suffer from premature localised pull-through failures in the batten to rafter connections during high wind events. A recent study proposed a suitable design equation for the pull-through failures of thin steel roof battens. However, it was limited to static wind uplift loading. In contrast, most cyclone/storm events produce cyclic wind uplift forces on roofs for a significantly long period, thus causing premature fatigue pull-through failures at lower loads. Therefore, a series of constant amplitude cyclic load tests was conducted on small and full scale roof panels made of a commonly used industrial roof batten to develop their S-N curves. A series of multi-level cyclic tests, including the recently introduced low-high-low (LHL) fatigue loading test, was also undertaken to simulate a design cyclone. Using the S-N curves, the static pull-through design capacity equation was modified to include the effects of fatigue. Applicability of Miner’s rule was evaluated in order to predict the fatigue damage caused by multi-level cyclic tests such as the LHL test, and suitable modifications were made. The combined use of the modified Miner’s law and the S-N curve of roof battens will allow a conservative estimation of the fatigue design capacity of roof battens without conducting the LHL tests simulating a design cyclone. This paper presents the details of this study, and the results.

Feasibility of a stepped wedge cluster RCT and concurrent observational sub-study to evaluate the effects of modified ward night lighting on inpatient fall rates and sleep quality: A protocol for a pilot trial

Background: Falls among hospitalised patients impose a considerable burden on health systems globally and prevention is a priority. Some patient-level interventions have been effective in reducing falls, but others have not. An alternative and promising approach to reducing inpatient falls is through the modification of the hospital physical environment and the night lighting of hospital wards is a leading candidate for investigation. In this pilot trial, we will determine the feasibility of conducting a main trial to evaluate the effects of modified night lighting on inpatient ward level fall rates. We will test also the feasibility of collecting novel forms of patient level data through a concurrent observational sub-study. Methods/design: A stepped wedge, cluster randomised controlled trial will be conducted in six inpatient wards over 14 months in a metropolitan teaching hospital in Brisbane (Australia). The intervention will consist of supplementary night lighting installed across all patient rooms within study wards. The planned placement of luminaires, configurations and spectral characteristics are based on prior published research and pre-trial testing and modification. We will collect data on rates of falls on study wards (falls per 1000 patient days), the proportion of patients who fall once or more, and average length of stay. We will recruit two patients per ward per month to a concurrent observational sub-study aimed at understanding potential impacts on a range of patient sleep and mobility behaviour. The effect on the environment will be monitored with sensors to detect variation in light levels and night-time room activity. We will also collect data on possible patient-level confounders including demographics, pre-admission sleep quality, reported vision, hearing impairment and functional status. Discussion: This pragmatic pilot trial will assess the feasibility of conducting a main trial to investigate the effects of modified night lighting on inpatient fall rates using several new methods previously untested in the context of environmental modifications and patient safety. Pilot data collected through both parts of the trial will be utilised to inform sample size calculations, trial design and final data collection methods for a subsequent main trial.

Relations between chronic regulatory focus and future time perspective: Results of a cross-lagged structural equation model

Future time perspective - the way individuals perceive their remaining time in life - importantly influences socio-emotional goals and motivational outcomes. Recently, researchers have called for studies that investigate relationships between personality and future time perspective. Using a cross-lagged panel design, this study investigated effects of chronic regulatory focus dimensions (promotion and prevention orientation) on future time perspective dimensions (focus on opportunities and limitations). Survey data were collected two times, separated by a 3. month time lag, from 85 participants. Results of structural equation modeling showed that promotion orientation had a positive lagged effect on focus on opportunities, and prevention orientation had a positive lagged effect on focus on limitations.

Social interaction and reflection for behaviour change

This article introduces the theme issue on social interaction and reflection for behaviour change. A large body of research exists on systems designed to help users in changing their behaviours, for instance, to exercise more regularly or to reduce energy consumption. Increasingly, these systems focus on multiple users, often to encourage open-ended reflection rather than prescribing a particular course of action. As background for this theme issue, this article presents a literature review on behaviour change support systems that focus on social interaction and reflection. The review highlights five key approaches amongst these systems: social traces, social support, collective use, reflection-in-action, and reflection-on-action. Each approach offers unique benefits, but also challenges for the design of behaviour change support systems. We highlight how the articles in this theme issue contribute to our current understanding of these five approaches, and beyond that, set out some broad directions for future work.