Abstract

This paper presents the characteristics of the different stages in the evolution of the wake of a circular cylinder rolling without slipping along a wall at constant speed, acquired through numerical stability analysis and two-and three-dimensional numerical simulations. Reynolds numbers between 30 and 300 are considered. Of importance in this study is the transition to three-dimensionality from the underlying two-dimensional periodic flow and, in particular, the way that the associated transitions influence the fluid forces exerted on the cylinder, and the development and the structure of the wake. It is found that the steady two-dimensional flow becomes unstable to threedimensional perturbations at Re c,3D = 37, and that the transition to unsteady twodimensional flow -or periodic vortex shedding -occurs at Re c,2D = 88, thus validating and refining the results of Stewart et al. (2010). The main focus here is for Reynolds numbers beyond the transition to unsteady flow at Re c,2D = 88. From impulsive start up, the wake almost immediately undergoes transition to a periodic two-dimensional wake state, which, in turn, is three-dimensionally unstable. Thus, the previous threedimensional stability analysis based on the two-dimensional steady flow provides only an element of the full story. Floquet analysis based on the periodic two-dimensional flow was undertaken and new three-dimensional instability modes were revealed. The results suggest that an impulsively started cylinder rolling along a surface at constant velocity for Re 90 will result in the rapid development of a periodic two-dimensional wake that will be maintained for a considerable time prior to the wake undergoing threedimensional transition. Of interest, the mean lift and drag coefficients obtained from full three-dimensional simulations match predictions from two-dimensional simulations to within a few percent.

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Between June and August 2020, an agent-based model was used to project rates of COVID-19 infection incidence and cases diagnosed as positive from 15 September to 31 October 2020 for 72 geographic settings. Five scenarios were modelled: a baseline scenario where no future changes were made to existing restrictions, and four scenarios representing small or moderate changes in restrictions at two intervals. Post hoc, upper and lower bounds for number of diagnosed Covid-19 cases were compared with actual data collected during the prediction window. A regression analysis with 17 covariates was performed to determine correlates of accurate projections. It was found that the actual data fell within the lower and upper bounds in 27 settings and out of bounds in 45 settings. The only statistically significant predictor of actual data within the predicted bounds was correct assumptions about future policy changes (OR 15.04; 95% CI 2.20–208.70; p = 0.016). Frequent changes in restrictions implemented by governments, which the modelling team was not always able to predict, in part explains why the majority of model projections were inaccurate compared with actual outcomes and supports revision of projections when policies are changed as well as the importance of modelling teams collaborating with policy experts.

IntroductionWith limited resources, attaining maximal average health service coverage can be at odds with maximising equity which attempts to promote greater reach among underserved populations. In this study, we examined the trade-offs in immunisation coverage levels and equity for children under 5 years of age in Pakistan across various subpopulations who can be targeted with different combinations of immunisation service modalities.MethodsWe conducted a detailed costing exercise across 16 geographically and demographically diverse districts in Pakistan. These data were the basis for (a) technical efficiency benchmarking via Data Envelopment Analysis to identify potential efficiency gains by location, delivery model and cost ingredient; (b) allocative efficiency optimisation modelling to understand how resource allocations could be optimised and to devise recommended budget allocations and operational metrics. Finally, the hypothetical overall efficiency gains attainable were estimated if available resources were allocated with the optimal emphases, and if service delivery models operated at productivity levels at the benchmarked frontier of efficiency.ResultsBenchmarking suggests that ~44% of delivery models are running efficiently and 37% are highly inefficient. While coverage and equity are usually at odds, surprisingly, the optimisation modelling revealed that substantial improvements in equity between subpopulations does not necessarily cost very much in overall immunisation coverage: theoretically, equity can be achieved while still attaining close to maximal immunisation coverage. Overall, analyses suggest greater emphases should be placed on outreach delivery models which particularly target rural areas and slum populations.ConclusionThe unit cost differentials within districts are not sufficiently large for there to be a large reduction in potential Fully Immunised Children coverage if one focuses on maximising equity. However, reallocations of programme budgets can have a significant impact on equity outcomes, particularly at current low spending amounts. Therefore, it is recommended to address equity as the key objective in national immunisation programming.

Introduction To retrospectively assess the accuracy of a mathematical modelling study that projected the rate of COVID-19 diagnoses for 72 locations worldwide in 2021, and to identify predictors of model accuracy. Methods Between June and August 2020, an agent-based model was used to project rates of COVID-19 infection incidence and cases diagnosed as positive from 15 September to 31 October 2020 for 72 geographic settings. Five scenarios were modelled: a baseline scenario where no future changes were made to existing restrictions, and four scenarios representing small or moderate changes in restrictions at two intervals. Post hoc, upper and lower bounds for number of diagnosed Covid-19 cases were compared with actual data collected during the prediction window. A regression analysis with 17 covariates was performed to determine correlates of accurate projections. Results The actual data fell within the lower and upper bounds in 27 settings and out of bounds in 45 settings. The only statistically significant predictor of actual data within the predicted bounds was correct assumptions about future policy changes (OR = 15.04; 95%CI 2.20-208.70; p=0.016). Conclusions For this study, the accuracy of COVID-19 model projections was dependent on whether assumptions about future policies are correct. Frequent changes in restrictions implemented by governments, which the modelling team was not always able to predict, in part explains why the majority of model projections were inaccurate compared with actual outcomes and supports revision of projections when policies are changed as well as the importance of policy experts collaborating on modelling projects.

Between June and August 2020, an agent-based model was used to project rates of COVID-19 infection incidence and cases diagnosed as positive from 15 September to 31 October 2020 for 72 geographic settings. Five scenarios were modelled: a baseline scenario where no future changes were made to existing restrictions, and four scenarios representing small or moderate changes in restrictions at two intervals. Post hoc, upper and lower bounds for number of diagnosed Covid-19 cases were compared with actual data collected during the prediction window. A regression analysis with 17 covariates was performed to determine correlates of accurate projections. It was found that the actual data fell within the lower and upper bounds in 27 settings and out of bounds in 45 settings. The only statistically significant predictor of actual data within the predicted bounds was correct assumptions about future policy changes (OR = 15.04; 95%CI 2.20-208.70; p = 0.016). Frequent changes in restrictions implemented by governments, which the modelling team was not always able to predict, in part explains why the majority of model projections were inaccurate compared with actual outcomes and supports revision of projections when policies are changed as well as the importance of modelling teams collaborating with policy experts.

A comprehensive investigation, using experimental, computational and analytic methods, is reported on the motion of, and the forces on, spheres of different density ratios rolling freely down an incline in a fluid under gravity. The Reynolds number, based on sphere diameter and terminal velocity, ranged up to 1000 for the experiments, and up to 250 for the computer simulations. A modified Reynolds number, incorporating the density ratio, gravitational acceleration and angle of incline, was found to govern the saturated state of the flow. Transition from steady to unsteady flow was sensitive to mass ratio, with lighter spheres undergoing earlier transition. Indeed, positively buoyant spheres develop cross-slope oscillations prior to the onset of shedding. Also of interest, the transition to chaotic wake flow occurs at Reynolds numbers lower than for a sphere forced to roll at a constant speed. In addition to the average sphere motion, flow-induced vibrations were predicted and measured, with quasi-periodic lateral oscillations found to increase as the flow became more unstable, and to decrease with increased density ratio. The study confirms the time-averaged results of a previous experimental study, although closer inspection shows sensitivity to the relative surface roughness of the sphere and plane in experiments; this sensitivity is masked in typical log–log plots of drag against Reynolds number. Physical surface roughness appears to play a role analogous to the necessary imposed gap between the sphere and plane in computations, removing the singularity in drag that would prevent rolling for an incompressible fluid and perfectly smooth surfaces.