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We study the dynamical system of a two-dimensional, forced, stratified mixing layer at finite Reynolds number
, and Prandtl number
. We consider a hyperbolic tangent background velocity profile in the two cases of hyperbolic tangent and uniform background buoyancy stratifications, in a domain of fixed, finite width and height. 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,
, is less than a certain critical value
, 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
. Bifurcation diagrams are produced using branch continuation, and we explore how these diagrams change with varying
. In particular, when
is sufficiently high we find that finite-amplitude Kelvin–Helmholtz billows exist when
for the background flow, which 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
, which complicates the dynamics.
Every four years leading researchers gather to survey the latest developments in all aspects of group theory. Initially held in St Andrews, these meetings have become the premier forum for group theory across the whole of the UK. Since 1981, the proceedings of 'Groups St Andrews' have provided a regular snapshot of the state-of-the-art in group theory and helped to shape the direction of research in the field. This volume contains papers from the 2017 meeting held in Birmingham. It includes expository articles from the invited speakers, and further surveys contributed by the participants. Topics include: generation of finite simple groups, block theory, fusion systems, algebraic groups, one-relator groups, geometric group theory, and Beauville groups.
is the prime power decomposition of an integer v, and we define the arithmetic function n(v) by
then it is known, MacNeish (10) and Mann (11), that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v. We shall denote by N(v) the maximum possible number of mutually orthogonal Latin squares of order v. Then the Mann-MacNeish theorem can be stated as
MacNeish conjectured that the actual value of N(v) is n(v).
We reviewed all patients who were supported with extracorporeal membrane oxygenation and/or ventricular assist device at our institution in order to describe diagnostic characteristics and assess mortality.
A retrospective cohort study was performed including all patients supported with extracorporeal membrane oxygenation and/or ventricular assist device from our first case (8 October, 1998) through 25 July, 2016. The primary outcome of interest was mortality, which was modelled by the Kaplan–Meier method.
A total of 223 patients underwent 241 extracorporeal membrane oxygenation runs. Median support time was 4.0 days, ranging from 0.04 to 55.8 days, with a mean of 6.4±7.0 days. Mean (±SD) age at initiation was 727.4 days (±146.9 days). Indications for extracorporeal membrane oxygenation were stratified by primary indication: cardiac extracorporeal membrane oxygenation (n=175; 72.6%) or respiratory extracorporeal membrane oxygenation (n=66; 27.4%). The most frequent diagnosis for cardiac extracorporeal membrane oxygenation patients was hypoplastic left heart syndrome or hypoplastic left heart syndrome-related malformation (n=55 patients with HLHS who underwent 64 extracorporeal membrane oxygenation runs). For respiratory extracorporeal membrane oxygenation, the most frequent diagnosis was congenital diaphragmatic hernia (n=22). A total of 24 patients underwent 26 ventricular assist device runs. Median support time was 7 days, ranging from 0 to 75 days, with a mean of 15.3±18.8 days. Mean age at initiation of ventricular assist device was 2530.8±660.2 days (6.93±1.81 years). Cardiomyopathy/myocarditis was the most frequent indication for ventricular assist device placement (n=14; 53.8%). Survival to discharge was 42.2% for extracorporeal membrane oxygenation patients and 54.2% for ventricular assist device patients. Kaplan–Meier 1-year survival was as follows: all patients, 41.0%; extracorporeal membrane oxygenation patients, 41.0%; and ventricular assist device patients, 43.2%. Kaplan–Meier 5-year survival was as follows: all patients, 39.7%; extracorporeal membrane oxygenation patients, 39.7%; and ventricular assist device patients, 43.2%.
This single-institutional 18-year review documents the differential probability of survival for various sub-groups of patients who require support with extracorporeal membrane oxygenation or ventricular assist device. The indication for mechanical circulatory support, underlying diagnosis, age, and setting in which cannulation occurs may affect survival after extracorporeal membrane oxygenation and ventricular assist device. The Kaplan–Meier analyses in this study demonstrate that patients who survive to hospital discharge have an excellent chance of longer-term survival.
The authors review their experiences of metabolic profiles in dairy herds, with a view to assessing whether metabolic stress is a problem in Great Britain at present. Many cows show elevated blood beta-hydroxybutyrate concentration, indicating energy deficit, or elevated urea levels, indicating an imbalance between energy and protein in the rumen but at present there is no evidence that high-yielding cows in commercial herds show more metabolic stress than low-yielding cows. The authors suggest that more cows could suffer metabolic stress in the future, unless farmers’ ability to feed and manage dairy cows develops as rapidly as genetic selection for high milk yield.
Children with poor mental health often struggle at school. The relationship between childhood psychiatric disorder and exclusion from school has not been frequently studied, but both are associated with poor adult outcomes. We undertook a secondary analysis of the British Child and Adolescent Mental Health Surveys from 2004 and its follow-up in 2007 to explore the relationship between exclusion from school and psychopathology. We predicted poorer mental health among those excluded.
Psychopathology was measured using the Strengths and Difficulties Questionnaire, while psychiatric disorder was assessed using the Development and Well-Being Assessment and applying Diagnostic and Statistical Manual of Mental Disorders Fourth Edition (DSM IV) criteria. Exclusion from school and socio-demographic characteristics were reported by parents. Multi-variable regression models were used to examine the impact of individual factors on exclusion from school or psychological distress.
Exclusion from school was commoner among boys, secondary school pupils and those living in socio-economically deprived circumstances. Poor general health and learning disability among children and poor parental mental health were also associated with exclusion. There were consistently high levels of psychological distress among those who had experienced exclusion at baseline and follow-up.
We detected a bi-directional association between psychological distress and exclusion. Efforts to identify and support children who struggle with school may therefore prevent both future exclusion and future psychiatric disorder.
Endeavours to control urogenital schistosomiasis on Unguja Island (Zanzibar) have focused on school-aged children. To assess the impact of an associated health education campaign, the supervised use of the comic-strip medical booklet Juma na Kichocho by Class V pupils attending eighteen primary schools was investigated. A validated knowledge and attitudes questionnaire was completed at baseline and repeated one year later following the regular use of the booklet during the calendar year. A scoring system (ranging from 0.0 to 5.0) measured children’s understandings of schistosomiasis and malaria, with the latter being a neutral comparator against specific changes for schistosomiasis. In 2006, the average score from 751 children (328 boys and 423 girls) was 2.39 for schistosomiasis and 3.03 for malaria. One year later, the score was 2.43 for schistosomiasis and 2.70 for malaria from 779 children (351 boys and 428 girls). As might be expected, knowledge and attitudes scores for schistosomiasis increased (+0.05), but not as much as originally hoped, while the score for malaria decreased (−0.33). According to a Kolmogorov–Smirnov test, neither change was statistically significant. Analysis also revealed that 75% of school children misunderstood the importance of reinfection after treatment with praziquantel. These results are disappointing. They demonstrate that it is mistaken to assume that knowledge conveyed in child-friendly booklets will necessarily be interpreted, and acted upon, in the way intended. If long-term sustained behavioural change is to be achieved, health education materials need to engage more closely with local understandings and responses to urogenital schistosomiasis. This, in turn, needs to be part of the development of a more holistic, biosocial approach to the control of schistosomiasis.
This paper considers science aspects of a 1980 spacecraft reconnaissance of Comet Encke. The mission discussed is a ballistic flyby (more exactly, a fly-through) of P/Encke, using either a spin-stabilized spacecraft, without despin of instruments, or a 3-axis-stabilized spacecraft. Celestial mechanics and imaging aspects of such a mission have been considered in more detail by Bender (1) and by Jaffe et al (2), respectively. Engineering designs (3, 4) and more detailed accounts of science aspects are given in other documents. A different approach to an Encke ballistic flyby has been suggested by Farquahar et al (5). Yeomans (6) has considered ephemeris uncertainties associated with such missions.
The present observational problem of understanding the nature and origin of comets is analogous to that we would face in attempting to understand a planet and its atmosphere if we possessed only data on its ionosphere and exosphere. Virtually everything we can observe remotely is a part of the rapidly escaping gas and dust atmosphere of the comet.
Marine shelf lagoon deposits of Middle Ordovician age in Tennessee contain the record of repeated ecological successions which began on soft, azoic, terrigenous muds and progressed to a complex bryozoan-brachiopod community. The stages of succession formed a skeletal limestone bed. The process led to an interbedded shale-limestone stratigraphic sequence. The pioneer was the brachiopod Strophomena basilica which paved the soft mud with accumulated shells. Encrusting bryozoans colonized this shell pavement and were followed by ramose bryozoans. The final stages of succession included bryozoans, gastropods, pelecypods, and pelmatozoans but were dominated by the brachiopod Rostricellula rostrata.
Measurements of total length, width, length to growth lines (Strophomena only), and thickness (Rostricellula only) were used to generate growth-rate, and survivorship curves for these two species. Strophomena shows low juvenile mortality, a moderate, linear growth-rate, and increased mortality in later ages. Rostricellula shows relatively higher juvenile mortality, a rapid non-linear growth rate, and nearly constant mortality. These attributes are contrary to expectations derived from theory, but can be understood in the light of autecological factors for each species. Adaptation to soft substrata was the primary factor controlling population dynamics in Strophomena, and crowding was the main factor in Rostricellula.
The region of the 8200 Å Band of H2O was studied in spectra of Venus obtained with an echelle grating spectrograph operated at an altitude of 14.6 km in the NASA Learjet research aircraft. Taking advantage of low foreground absorption, observing at a time of velocity quadrature, differential spectroscopy with respect to lunar spectra, and spectrum averaging, we establish a value of H2O of 3 ± 20 μ for the total path over the entire disk. This value differs from earlier studies of the integrated disk but supports the low values recently derived from infrared bands and by very high spectral resolution groundbased studies.
These results establish that the average value over the entire disk is quite low but allows that locally larger values may exist as reported by Barker. A more complete description of this work appeared in Icarus21 (1974), 213.
Avian diet selection is hypothesized to be sensitive to seasonal changes in breeding status, but few tests exist for frugivorous tropical birds. Frugivorous birds provide an interesting test case because fruits are relatively deficient in minerals critical for reproduction. Here, we quantify annual patterns of fruit availability and diet for two frugivorous hornbill (Bucerotidae) species over a 5.5-y period to test for patterns of diet selection. Data from the lowland tropical rain forest of the Dja Reserve, Cameroon, are used to generate two nutritional indices. One index estimates the nutrient concentration of the diet chosen by Ceratogymna atrata and Bycanistes albotibialis on a monthly basis using 3165 feeding observations combined with fruit pulp sample data. The second index is an estimate of nutrient concentration of a non-selective or neutral diet across the study area based on tree fruiting phenology, vegetation survey and fruit-pulp sample data. Fifty-nine fruit pulp samples representing 40 species were analysed for 16 nutrient categories to contribute to both indices. Pulp samples accounted for approximately 75% of the observed diets. The results support expected patterns of nutrient selection. The two hornbill species selected a diet rich in calcium during the early breeding season (significantly so for B. albotibialis in July and August). Through the brooding and fledging periods, they switched from a calcium-rich diet to one rich in iron and caloric content as well as supplemental protein in the form of invertebrates. Calcium, the calcium to phosphorus ratio and fat concentration were the strongest predictors of breeding success (significant for calcium and Ca:P for B. albotibialis in June). We conclude that hornbills actively select fruit based on nutritional concentration and mineral concentration and that the indices developed here are useful for assessing frugivore diet over time.
The Magnetoresistance (MR), Magnetic properties, and crystal structure of dc magnetron sputtered CO/Ag periodic multilayers have been investigated. The Co layer thickness was fixed at -30 Å while the thickness of the Ag layer was systematically varied. ‘Giant’ magnetoresistance was observed. The MR ratio has been found to decline monotonically with increasing Ag thickness in the range 30 Å to 107 Å. Although the maximum room temperature MR ratio is a Modest 4.78%, a more technologically significant measurement of field sensitivity (MR ratio/FWHM of the MR vs. H peak) is a promising 0.1%/Oe at its best. The effect of the number of bilayer units has also been examined and no substantial differences were noted between multilayers containing 8, 9, and 10 bilayer units. Coercivities as determined by both magnetometer and the splitting of the MR peaks are in agreement and increase from 25 to 38 Oe with increasing Ag thickness. Evidence for antiferromagnetic coupling is apparent in the hysteresis loops. High angle X-ray diffractometry (HXRD) in the θ-2θ mode revealed a strong Ag (111) texture in the film, with satellite peaks indicating a layered structure. Low angle XRD (LXRD) also yielded broad superlattice peaks in all samples at least to the second order.
Although Much has been published on giant Magnetoresistance (GMR) in co-deposited thin films [1–4], only little  has been published on the structure-property relationships limiting the effect. Here, we report the results of microstructural characterization of NiFeAg thin films that exhibit a GMR effect. The as-deposited films show a sizeable GMR effect. The Maximum GMR effect observed was 6.4% with -4k0e FWHM of the 6P/P peak. Upon annealing these films, the GMR at first increases, and then decreases. We present microstructural evidence from TEM and XRD, amongst other techniques, which shows that this is a consequence of the initial NiFeAg thin film agglomerating into NiFe grains in a predominantly Ag segregant Matrix. Upon extended annealing, excessive grain growth leads to a decrease in the GMR as predicted by the model of Berkowitz, et al. .
The phenomenon of giant magnetoresistance (GMR), previously measured only in multilayer films comprising ferromagnetic layers separated by nonmagnetic spacers, has recently been observed in single layer ‘granular’ alloy thin films prepared by cosputtering a ferromagnet and a nonmagnet which tend to phase separate (cluster) under equilibrium conditions. We have systematically studied the magnetoresistance of two new phase separating GMR systems (Ni66Fe16Co18-Ag and Co9oFelo-Ag) both of which exhibit large room temperature GMR (>11% and >14%, respectively). We have also attempted to influence the details of the field dependence of the magnetoresistance in the previously studied Co-Ag system by employing novel processing methods including interrupted sputtering and layering of the Co-Ag alloy with Cu spacers.
A Model for the field dependence of giant Magnetoresistance (GMR) in ‘granular’ co-sputtered alloy thin films (based on a relatively simple spin-dependent scattering concept appropriate to superparamagnetic and weakly ferromagnetic films) is applied to new experimental data from the Co90Fe10-Ag system. The Model and the experimental data can be shown to compare very well with the help of a single adjustable parameter related to spin correlation of adjacent Co-Fe clusters. A careful fit of field-dependent MR data and theory leads to a fairly reliable determination of spin-cluster radius. An analysis of the relative permeability of granular GMR films derived from the generalized form of the Clausius-Mossoti relationship is also presented. For a non-Magnetic Matrix the effective relative permeability is shown to be materials independent. The permeability model is applied to Co-Au granular films.