The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

Abstract EPSRC DT

Kelvin-Helmholtz billows above Richardson number 1/4

We study the dynamical system of a forced stratified mixing layer at finite Reynolds number $Re$, and Prandtl number $Pr=1$. We consider a hyperbolic tangent background velocity profile in the two cases of hyperbolic tangent and uniform background buoyancy stratifications. The system is forced in such a way that these background profiles are a steady solution of the governing equations. As is well-known, if the minimum gradient Richardson number of the flow, $Ri_m$, is less than a certain critical value $Ri_c$, the flow is linearly unstable to Kelvin-Helmholtz instability in both cases. Using Newton-Krylov iteration, we find steady, two-dimensional, finite amplitude elliptical vortex structures, i.e. `Kelvin-Helmholtz billows', existing above $Ri_c$. Bifurcation diagrams are produced using branch continuation, and we explore how these diagrams change with varying $Re$. In particular, when $Re$ is sufficiently high we find that finite amplitude Kelvin-Helmholtz billows exist at $Ri_m>1/4$, where the flow is linearly stable by the Miles-Howard theorem. For the uniform background stratification, we give a simple explanation of the dynamical system, showing the dynamics can be understood on a two-dimensional manifold embedded in state space, and demonstrate the cases in which the system is bistable. In the case of a hyperbolic tangent stratification, we also describe a new, slow-growing, linear instability of the background profiles at finite $Re$, which complicates the dynamics

Private Schooling, Educational Transitions, and Early Labour Market Outcomes: Evidence from Three Anglophone Countries

This article considers the extent to which private-state school differences in post-secondary outcomes can be explained by family background, secondary school achievement, or neither of the above. We find that privately educated children’s more advantaged family backgrounds and higher levels of school achievement are the main reasons why this group is more likely to enter university and work in professional jobs. However, even after accounting for family background and high school achievement, non-trivial private-state school differences in later lifetime outcomes remain. Empirical evidence is presented for three industrialized nations (Australia, England, and the United States), with broadly similar patterns of association observed within each

Working memory capacity and surgical performance whilst exposed to mild hypoxic hypoxaemia (3000m)

INTRODUCTION: Medical Emergency Response Team (MERT) helicopters fly at altitudes of 3,000m in Afghanistan (9,843ft). Civilian hospitals and disaster-relief surgical teams may have to operate at such altitudes or even higher. Mild hypoxia has been seen to affect the performance of novel tasks at flight levels as low as 5,000ft. Aeromedical teams frequently work in unpressurised environments; it is important to understand the implications of this mild hypoxia and investigate whether supplementary oxygen systems are required for some or all of the team members. METHODS: Ten UK orthopaedic surgeons were recruited and in a double blind randomised experimental protocol, were acutely exposed for 45 minutes to normobaric hypoxia (fraction of inspired oxygen (FiO2) ~14.1% - equivalent to 3000m/10,000ft) or normobaric normoxia (sea-level). Basic physiological parameters were recorded. Subjects completed validated tests of verbal working memory capacity (VWMC) and also applied an orthopaedic external fixator (Hoffmann® 3, Stryker UK) to a plastic tibia under test conditions. RESULTS: Significant hypoxia was induced with the reduction of FiO2 to ~14.1% (SpO2 87% vs. 98%). No effect of hypoxia on VWMC was observed. The pin-divergence score (a measure of frame asymmetry) was significantly greater in hypoxic conditions (4.6mm) compared to sea level (3.0mm), there was no significant difference in the penetrance depth (16.9 vs. 17.2mm). One frame would have failed early. DISCUSSION: We believe that surgery at an altitude of 3000m when unacclimated individuals are acutely exposed to atmospheric hypoxia for 45 minutes, can likely take place without supplemental oxygen use but further work is required

Simultaneous determination of wave speed and arrival time of reflected waves using the pressure-velocity loop

This is the post print version of the article. The official published version can be found at the link below.In a previous paper we demonstrated that the linear portion of the pressure–velocity loop (PU-loop) corresponding to early systole could be used to calculate the local wave speed. In this paper we extend this work to show that determination of the time at which the PU-loop first deviates from linearity provides a convenient way to determine the arrival time of reflected waves (Tr). We also present a new technique using the PU-loop that allows for the determination of wave speed and Tr simultaneously. We measured pressure and flow in elastic tubes of different diameters, where a strong reflection site existed at known distances away form the measurement site. We also measured pressure and flow in the ascending aorta of 11 anaesthetised dogs where a strong reflection site was produced through total arterial occlusion at four different sites. Wave speed was determined from the initial slope of the PU-loop and Tr was determined using a new algorithm that detects the sampling point at which the initial linear part of the PU-loop deviates from linearity. The results of the new technique for detecting Tr were comparable to those determined using the foot-to-foot and wave intensity analysis methods. In elastic tubes Tr detected using the new algorithm was almost identical to that detected using wave intensity analysis and foot-to-foot methods with a maximum difference of 2%. Tr detected using the PU-loop in vivo highly correlated with that detected using wave intensity analysis (r 2 = 0.83, P < 0.001). We conclude that the new technique described in this paper offers a convenient and objective method for detecting Tr, and allows for the dynamic determination of wave speed and Tr, simultaneously

Performance optimization of a leagility inspired supply chain model: a CFGTSA algorithm based approach

Lean and agile principles have attracted considerable interest in the past few decades. Industrial sectors throughout the world are upgrading to these principles to enhance their performance, since they have been proven to be efficient in handling supply chains. However, the present market trend demands a more robust strategy incorporating the salient features of both lean and agile principles. Inspired by these, the leagility principle has emerged, encapsulating both lean and agile features. The present work proposes a leagile supply chain based model for manufacturing industries. The paper emphasizes the various aspects of leagile supply chain modeling and implementation and proposes a new Hybrid Chaos-based Fast Genetic Tabu Simulated Annealing (CFGTSA) algorithm to solve the complex scheduling problem prevailing in the leagile environment. The proposed CFGTSA algorithm is compared with the GA, SA, TS and Hybrid Tabu SA algorithms to demonstrate its efficacy in handling complex scheduling problems

Measuring co-authorship and networking-adjusted scientific impact

Appraisal of the scientific impact of researchers, teams and institutions with productivity and citation metrics has major repercussions. Funding and promotion of individuals and survival of teams and institutions depend on publications and citations. In this competitive environment, the number of authors per paper is increasing and apparently some co-authors don't satisfy authorship criteria. Listing of individual contributions is still sporadic and also open to manipulation. Metrics are needed to measure the networking intensity for a single scientist or group of scientists accounting for patterns of co-authorship. Here, I define I1 for a single scientist as the number of authors who appear in at least I1 papers of the specific scientist. For a group of scientists or institution, In is defined as the number of authors who appear in at least In papers that bear the affiliation of the group or institution. I1 depends on the number of papers authored Np. The power exponent R of the relationship between I1 and Np categorizes scientists as solitary (R>2.5), nuclear (R=2.25-2.5), networked (R=2-2.25), extensively networked (R=1.75-2) or collaborators (R<1.75). R may be used to adjust for co-authorship networking the citation impact of a scientist. In similarly provides a simple measure of the effective networking size to adjust the citation impact of groups or institutions. Empirical data are provided for single scientists and institutions for the proposed metrics. Cautious adoption of adjustments for co-authorship and networking in scientific appraisals may offer incentives for more accountable co-authorship behaviour in published articles.Comment: 25 pages, 5 figure

Ultrasound-guided large-core needle biopsies of breast lesions: analysis of 962 cases to determine the number of samples for reliable tumour classification

The objective of this one-institutional study was to determine the number of large-core needle biopsies (LCNB), under three-dimensional ultrasound (3D-US) validation, that are sufficient to obtain a reliable histological diagnosis of a sonographically detectable breast lesion. Over an 28-month period, 962 sonographically guided LCNB were performed under 3D-US validation to assess 962 breast lesions. All biopsies were carried out with an automated core biopsy device fitted with 14-gauge (22 mm excursion) needles. Data of 962 biopsied breast lesions were gathered. Surgical follow-up was available for 659 lesions. Breast malignancies were diagnosed by ultrasound-guided LCNB with a sensitivity of 98.2% by performing three cores per lesion. In few cases, the open surgical specimen revealed the presence of invasive carcinomas in contrast to initial LNCB-based classification as ductal carcinomas in situ (DCIS, 11 lesions), lobular carcinoma in situ (one lesion), and atypical ductal hyperpasia (one lesion). Owing to disagreement between classification based on breast-imaging and histological findings, eight of these tumours were subsequently excised. Of the lesions that were removed at the patients' requests despite benign LCNB diagnosis, two were infiltrating carcinoma and one a DCIS. We demonstrate that three 3D-US-guided percutaneous core specimens are sufficient to achieve tissue for a reliable histological assessment of sonographically detectable breast lesions and allow the detection of malignancies with high sensitivity and low rate of false-negative diagnoses

Origin of Cosmic Magnetic Fields

We propose that the overlapping shock fronts from young supernova remnants produce a locally unsteady, but globally steady large scale spiral shock front in spiral galaxies, where star formation and therefore massive star explosions correlate geometrically with spiral structure. This global shock front with its steep gradients in temperature, pressure and associated electric fields will produce drifts, which in turn give rise to a strong sheet-like electric current, we propose. This sheet current then produces a large scale magnetic field, which is regular, and connected to the overall spiral structure. This rejuvenates the overall magnetic field continuously, and also allows to understand that there is a regular field at all in disk galaxies. This proposal connects the existence of magnetic fields to accretion in disks. We not yet address all the symmetries of the magnetic field here; the picture proposed here is not complete. X-ray observations may be able to test it already.Comment: 18 pages, no figures; to be published in Proc. Palermo Meeting Sept. 2002, Eds. N. G. Sanchez et al., The Early Universe and the Cosmic Microwave Background: Theory and Observation