An Engineering Approach to the Variable Fluid Property Problem in Free Convection

An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters

Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control

For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragus. A recent paper by Fiedler et al uses the normal form of a subcritical Hopf bifurcation to give a counterexample to this theorem. Using the Lorenz equations as an example, we demonstrate that the stabilization mechanism identified by Fiedler et al for the Hopf normal form can also apply to unstable periodic orbits created by subcritical Hopf bifurcations in higher-dimensional dynamical systems. Our analysis focuses on a particular codimension-two bifurcation that captures the stabilization mechanism in the Hopf normal form example, and we show that the same codimension-two bifurcation is present in the Lorenz equations with appropriately chosen Pyragus-type time-delayed feedback. This example suggests a possible strategy for choosing the feedback gain matrix in Pyragus control of unstable periodic orbits that arise from a subcritical Hopf bifurcation of a stable equilibrium. In particular, our choice of feedback gain matrix is informed by the Fiedler et al example, and it works over a broad range of parameters, despite the fact that a center-manifold reduction of the higher-dimensional problem does not lead to their model problem.Comment: 21 pages, 8 figures, to appear in PR

Details of Exact Low Prandtl Number Boundary-Layer Solutions for Forced and For Free Convection

A detailed report is given of exact (numerical) solutions of the laminar-boundary-layer equations for the Prandtl number range appropriate to liquid metals (0.003 to 0.03). Consideration is given to the following situations: (1) forced convection over a flat plate for the conditions of uniform wall temperature and uniform wall heat flux, and (2) free convection over an isothermal vertical plate. Tabulations of the new solutions are given in detail. Results are presented for the heat-transfer and shear-stress characteristics; temperature and velocity distributions are also shown. The heat-transfer results are correlated in terms of dimensionless parameters that vary only slightly over the entire liquid-metal range. Previous analytical and experimental work on low Prandtl number boundary layers is surveyed and compared with the new exact solutions

Progression from ocular hypertension to visual field loss in the English hospital eye service

Background There are more than one million National Health Service visits in England and Wales each year for patients with glaucoma or ocular hypertension (OHT). With the ageing population and an increase in optometric testing, the economic burden of glaucoma-related visits is predicted to increase. We examined the conversion rates of OHT to primary open-angle glaucoma (POAG) in England and assessed factors associated with risk of conversion. Methods Electronic medical records of 45 309 patients from five regionally different glaucoma clinics in England were retrospectively examined. Conversion to POAG from OHT was defined by deterioration in visual field (two consecutive tests classified as stage 1 or worse as per the glaucoma staging system 2). Cox proportional hazards models were used to examine factors (age, sex, treatment status and baseline intraocular pressure (IOP)) associated with conversion. Results The cumulative risk of conversion to POAG was 17.5% (95% CI 15.4% to 19.6%) at 5 years. Older age (HR 1.35 per decade, 95% CI 1.22 to 1.50, p<0.001) was associated with a higher risk of conversion. IOP-lowering therapy (HR 0.45, 95% CI 0.35 to 0.57, p<0.001) was associated with a lower risk of conversion. Predicted 5-year conversion rates for treated and untreated groups were 14.0% and 26.9%, respectively. Conclusion Less than one-fifth of OHT patients managed in glaucoma clinics in the UK converted to POAG over a 5-year period, suggesting many patients may require less intensive follow-up. Our study provides real-world evidence for the efficacy of current management (including IOP-lowering treatment) at reducing risk of conversion

Turbulent and Transitional Modeling of Drag on Oceanographic Measurement Devices

Computational fluid dynamic techniques have been applied to the determination of drag on oceanographic devices (expendable bathythermographs). Such devices, which are used to monitor changes in ocean heat content, provide information that is dependent on their drag coefficient. Inaccuracies in drag calculations can impact the estimation of ocean heating associated with global warming. Traditionally, ocean-heating information was based on experimental correlations which related the depth of the device to the fall time. The relation of time-depth is provided by a fall-rate equation (FRE). It is known that FRE depths are reasonably accurate for ocean environments that match the experiments from which the correlations were developed. For other situations, use of the FRE may lead to depth errors that preclude XBTs as accurate oceanographic devices. Here, a CFD approach has been taken which provides drag coefficients that are used to predict depths independent of an FRE

Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength $\epsilon_c$ with a scaling exponent $\gamma$. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling relation exists for $m$ couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength $\epsilon$. In addition, we have found that $\epsilon_c$ shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of R\"ossler and Lorenz oscillators.Comment: Accepted for Publication in Physical Review

Direct transition to high-dimensional chaos through a global bifurcation

In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori.The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.Comment: 7 page

Auditing service delivery in glaucoma clinics using visual field records: A feasibility study

© 2019 Author(s). Objective This study aimed to demonstrate that large-scale visual field (VF) data can be extracted from electronic medical records (EMRs) and to assess the feasibility of calculating metrics from these data that could be used to audit aspects of service delivery of glaucoma care. Method and analysis Humphrey visual field analyser (HFA) data were extracted from Medisoft EMRs from five regionally different clinics in England in November 2015, resulting in 602 439 records from 73 994 people. Target patients were defined as people in glaucoma clinics with measurable and sustained VF loss in at least one eye (HFA mean deviation (MD) outside normal limits ≥2 VFs). Metrics for VF reliability, stage of VF loss at presentation, speed of MD loss, predicted loss of sight years (bilateral VF impairment) and frequency of VFs were calculated. Results One-third of people (34.8%) in the EMRs had measurable and repeatable VF loss and were subject to analyses (n=25 760 patients). Median (IQR) age and presenting MD in these patients were 71 (61, 78) years and -6 (-10, -4) dB, respectively. In 19 264 patients with >4 years follow-up, median (IQR) MD loss was -0.2 (-0.8, 0.3) dB/year and median (IQR) intervals between VF examinations was 11 (8, 16) months. Metrics predicting loss of sight years and reliability of examinations varied between centres (p<0.001). Conclusion This study illustrates the feasibility of assessing aspects of health service delivery in glaucoma clinics through analysis of VF databases. Proposed metrics could be useful for blindness prevention from glaucoma in secondary care centres