On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations

Critical Binder cumulant in two-dimensional anisotropic Ising models

The Binder cumulant at the phase transition of Ising models on square lattices with various ferromagnetic nearest and next-nearest neighbour couplings is determined using mainly Monte Carlo techniques. We discuss the possibility to relate the value of the critical cumulant in the isotropic, nearest neighbour and in the anisotropic cases to each other by means of a scale transformation in rectangular geometry, to pinpoint universal and nonuniversal features.Comment: 7 pages, 4 figures, submitted to J. Phys.

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned

Aspirin delays the development of preeclampsia

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.BACKGROUND: In the Combined Multimarker Screening and Randomized Patient Treatment with Aspirin for Evidence-Based Preeclampsia Prevention (ASPRE) trial risks of preterm preeclampsia (PE) were obtained from the competing risk model. Consenting women with risks of greater than 1 in 100 were randomised to treatment with aspirin or placebo. The trial showed strong evidence of an effect (odds ratio 0.38, 95% confidence interval 0.20 to 0.74) on the incidence of preterm-PE, which was the primary outcome of ASPRE. There was a small and insignificant effect on the incidence of term-PE which was one of the secondary outcomes (odds ratio 0.95, 95% CI 0.64 to 1.39). These differential effects on term and preterm-PE could reflect a mechanism in which the action of aspirin is to delay the delivery with PE thereby converting what would, without treatment, be preterm-PE to term-PE. OBJECTIVE: To examine the hypothesis that the effect of aspirin is to delay the time of delivery with PE. STUDY DESIGN: This was an unplanned exploratory analysis of data from the ASPRE trial. The delay hypothesis predicts that in groups for which preterm-PE, without aspirin, were infrequent relative to term-PE, a reduction in term-PE would be expected because few cases of preterm-PE would be converted to term-PE. In contrast, in groups for which preterm-PE were frequent relative to term-PE, the conversion of preterm-PE to term-PE by aspirin would reduce or even reverse any effect on the incidence term-PE. This is examined using the ASPRE trial data by analysis of the effect of aspirin on the incidence of term-PE stratified according to the risk of preterm-PE at randomization. Given that women were included in ASPRE with risks of preterm PE > 1 in 100, a risk cut-off if 1 in 50 was used to define higher risk and lower risk strata. A statistical model in which the effect of aspirin is to delay the gestational age at delivery was fitted to the ASPRE trial data and the consistency of the predictions from this model with the observed incidence was demonstrated. RESULTS: In the lower risk group (<1 in 50), there was a reduction in the incidence of term-PE (odds ratio 0.62, 95% confidence interval 0.29 to 1.30). In contrast, in the higher risk group (≥1 in 50) there was a small increase in the incidence of term-PE (odds ratio 1.11, 95% confidence interval 0.71 to 1.75). Although these effects fail to achieve significance, they are consistent with the delay hypothesis. Within the framework of the aspirin-related delay hypothesis, the effect of aspirin was to delay the gestational age at delivery with PE by an estimated 4.4 weeks (95% CI 1.4 to 7.1 weeks) for those that in the placebo group would be delivered at 24 weeks and the effect decreased by an estimated 0.23 weeks (95% CI 0.021 to 0.40 weeks) for each week of gestation so that at 40+0 weeks the estimated delay was by 0.8 weeks (95% confidence interval -0.03 to 1.7 weeks). CONCLUSIONS: The ASPRE trial data are consistent with the hypothesis that aspirin delays the gestational age at delivery with PE.National Institute for Health Research (NIHR

An Urban Charging Infrastructure for electric road freight operations: A case study for Cambridge UK

A charging infrastructure for electric road freight operations is explored in this paper. The city of Cambridge UK was chosen for demonstration but the same methodology could be used for other cities as well. In particular, the five Park and Ride bus routes, the refuse collection operations and two home delivery operations were investigated. Real-time data about existing operations were collected to define accurate drive cycles. Different vehicles were modelled for each operation and their performance was evaluated over the defined drive cycles. Different charging infrastructures were proposed for each operation. The additional power demand, additional load, capital cost needed and the CO2 emissions savings for each case were calculated. The results were scaled up for the entire city and the implications for the electricity supply network were explored. It was shown that electrification of all road freight operations would increase the city’s power demand and electricity consumption by 6.3% and 8.1% respectively based on current figures. Such a system would cost £56.4 million at today’s prices and would result in accumulated savings of 164 MtCO2 by 2050.This research was supported by the EPSRC Grant EP/K00915X/1: “Centre for Sustainable Road Freight Transport” and the EPSRC Doctoral Training Award 1497982: “Wireless Electric Charge-on-the-move: An appraisal for the UK transport application.

Stability of Gaussian elimination without pivoting on tridiagonal Toeplitz matrices

AbstractUsing the simple vehicle of tridiagonal Toeplitz matrices, the question of whether one must pivot during the Gauss elimination procedure is examined. An exact expression for the multipliers encountered during the elimination process is given. It is then shown that for a prototype Helmholtz problem, one cannot guarantee that elimination without pivoting is stable

A national power infrastructure for charge-on-the-move: An appraisal for Great Britain

The electrification of road transportation is a necessary step for coping with climate change. Charge-on-the-move is considered to be a key enabling factor in moving towards electric vehicles. The development of individual charging devices for implementing in-motion charging has been rapid but their integration with the road infrastructure at national scale is still in need of more comprehensive consideration. This work aims to outline the performance requirements of a national power infrastructure suitable for implementing charge-on-the-move. From an estimation of electric vehicles’ power requirements in conjunction with Great Britain’s road traffic data the anticipated power demand is expected to be augmented by 16 GW. Furthermore, a simulation tool is proposed to investigate the application of dynamic charging and the effects of system design variables. Based on that, a possible charging layout is suggested. Such infrastructure involves 30 kW chargers, 1.5 m length apiece, installed every 2.1 m and 4.3 m on motorways and rural sections of road respectively. Finally, a strategic overview for Great Britain suggests that the installation of a nationwide charging infrastructure of this type could be economically viable. Indeed, the cost to develop the infrastructure to enable the electrification of 86% of car-miles in Great Britain is around £76 billion at present prices

Critical Binder cumulant for isotropic Ising models on square and triangular lattices

Using Monte Carlo techniques, the critical Binder cumulant U* of isotropic nearest-neighbour Ising models on square and triangular lattices is studied. For rectangular shapes, employing periodic boundary conditions, U* is found to show the same dependence on the aspect ratio for both lattice types. Similarly, applying free boundary conditions for systems with square as well as circular shapes for both lattices, the simulational findings are also consistent with the suggestion that, for isotropic Ising models with short-range interactions, U* depends on the shape and the boundary condition, but not on the lattice structure.Comment: 7 pages, 4 figures, submitted to J. Stat. Mec

Comparison of screening for pre-eclampsia at 31-34 weeks' gestation by sFlt-1/PlGF ratio and a method combining maternal factors with sFlt-1 and PlGF

Objective: To estimate the patient-specific risk of preeclampsia (PE) at 31-34 weeks’ gestation by a combination of maternal characteristics and medical history with multiple of the median (MoM) values of serum placental growth factor (PLGF) and serum soluble fms-like tyrosine kinase-1 (sFLT-1) and compare the performance of screening to that achieved by the sFLT-1 to PLGF ratio. Methods: This was a prospective observational study in women attending for a third-trimester ultrasound scan at 31-34 weeks as part of routine pregnancy care. We estimated the performance of screening of PE with delivery within four weeks of assessment (PE at <4 weeks) and PE from four weeks after assessment and up to 40 weeks’ gestation (PE at 4w-40GW) in screening by the sFLT-1 to PLGF ratio and by a to PLGF ratio and by a method utilizing Bayes theorem to combine maternal factors and MoM values of sFLT-1 and PLGF. The significance of difference in performance of screening between the method utilising Bayes theorem and that of the sFLT-1 to PLGF ratio was assessed by comparison of the areas under the receiver operating characteristic curves (AUROC). Results: The study population of 8,063 singleton pregnancies included 231 (2.9%) that subsequently developed PE. In the prediction of delivery with PE at <4 weeks the performance of the method utilising Bayes theorem was similar to that of the sFLT-1 to PLGF (AUROC: 0.987, 95%CI 0.979-0.995 vs. 0.988, 95%CI: 0.981-0.994; p=0.961). and at fixed fixed screen positive rate (SPR) of 3.9% the detection rate (DR) was 87.1% for both methods. In contrast, the performance of screening for delivery with PE at 4w-40GW was better with the method utilising Bayes theorem than with the sFLT-1 to PLGF ratio (AUROC: 0.884, 95%CI 0.854-0.914 vs. 0.818, 95%CI: 0.775--0.860 ; p<0.0001) and at total fixed SPR of 25.7% the DRs were 84.4% vs. 73.0%. Conclusion: At 31-34 weeks’ gestation the performance of screening for PE at <4 weeks from assessment by the method utilising Bayes theorem is similar to that of the sFLT-1 to PLGF ratio, but the former is superior to the latter in prediction of PE >>4 weeks

Comparison of different methods of measuring angle of progression in prediction of labor outcome

Objective: First, to compare the manual sagittal and para-sagittal and automated para-sagittal methods of measuring the angle of progression (AOP) by transperineal ultrasound during labor, and second, to develop models for the prediction of time-to-delivery and need for cesarean section (CS) for failure to progress (FTP) in a population of patients undergoing induction of labor. Methods: This was a prospective observational study of transperineal ultrasound on a cohort of 512 women with singleton pregnancies undergiong induction of labor. A random selection of 50 stored images was assessed for inter- and intra-observer reliability between methods. In the cases of vaginal delivery univariate linear, multivariate linear and quantile regression were performed to predict time-to-delivery. Univariate and multivariate binomial logistic regression were performed to predict CS for FTP in the first stage of labor. Results: The intra correlation coefficients (ICC) for the manual para-sagittal method for a single observer was 0.97 (CI 0.95-0.98) and for two observers was 0.96 (CI 0.93-0.98) indicating good reliability. The ICC for the sagittal method for a single observer was 0.93 (0.88-0.96) and for two observers was 0.74 (0.58-0.84) indicating moderate reliabilty for a single observer and poor reliability between two observers. Bland-Altman analysis demonstrated narrower limits of agreement for the manual para-saggittal approach than for the sagittal approach for both single and two observers. The automated para-sagittal method failed to capture an image in 19% of cases. The mean difference between sagittal and para-sagittal methods was 110. In pregnancies resulting in vaginal delivery, 54% of the variation in time-to-delivery was explained in a model combining parity, epidural and syntocinon use during labour and the sonographic findings of fetal head position and AOP. In the prediction of CS for FTP in the first stage of labour a model which combined maternal factors with the sonographic measurements of AOP and estimated fetal weight was superior to one utilising maternal factors alone (area under the curve 0.80 vs 0.76). Conclusions: First, the method of measuring AOP with greatest reliability is the manual parasagittal technique and future research should focus on this technique, second, over half of the variation in time to vaginal delivery can be explained by a model that combines maternal factors, pregnancy characteristics and ultrasound findings, and third, the ability of AOP to provide clinically useful prediction CS for FTP in the first stage of labour is limited