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We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of
partial differential equations and
algebraic conservation laws, for a system of
viscidas connected at
junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with
or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses.
We derive a mathematical model for the drawing of a two-dimensional thin sheet of viscous fluid in the direction of gravity. If the gravitational field is sufficiently strong, then a portion of the sheet experiences a compressive stress and is thus unstable to transverse buckling. We analyse the dependence of the instability and the subsequent evolution on the process parameters, and the mutual coupling between the weakly nonlinear buckling and the stress profile in the sheet. Over long time scales, the sheet centreline ultimately adopts a universal profile, with the bulk of the sheet under tension and a single large bulge caused by a small compressive region near the bottom, and we derive a canonical inner problem that describes this behaviour. The large-time analysis involves a logarithmic asymptotic expansion, and we devise a hybrid asymptotic–numerical scheme that effectively sums the logarithmic series.
We consider the spreading of a thin viscous droplet, injected through a finite region of a substrate, under the influence of surface tension. We neglect gravity and assume that there is a precursor layer covering the whole substrate and that the rate of injection is constant. We analyse the evolution of the film profile for early and late time, and obtain power-law dependencies for the maximum film thickness at the centre of the injection region and the position of an apparent contact line, which compare well with numerical solutions of the full problem. We relax the conditions on the injection rate to consider more general time-dependent and spatially varying forms. In the case of power-law injection of the form
, we observe a switch in the behaviour of the evolution of the film thickness for late time from increasing to decreasing at a critical value of
. We show that point-source injection can be treated as a limiting case of a finite-injection slot and the solutions exhibit identical behaviours for late time. Finally, we formulate the problem with thickness-dependent injection rate, discuss the behaviour of the maximum film thickness and the position of the apparent contact line and give power-law dependencies for these.
We investigate how a filter-medium microstructure influences filtration performance. We derive a theory that generalizes classical multiscale models for regular structures to account for filter media with more realistic microstructures, comprising random microstructures with polydisperse unidirectional fibres. Our multiscale model accounts for the fluid flow and contaminant transport at the microscale (over which the medium structure is fully resolved) and allows us to obtain macroscopic properties such as the effective permeability, diffusivity and fibre surface area. As the fibres grow due to contaminant adsorption, this leads to contact of neighbouring fibres. We propose an agglomeration algorithm that describes the resulting behaviour of the fibres upon contact, allowing us to explore the subsequent time evolution of the filter medium in a simple and robust way. We perform a comprehensive investigation of the influence of the filter-medium microstructure on filter performance in a spectrum of possible filtration scenarios.
Portugal has one of the highest rates of childhood overweight and obesity in Europe. However, little is known about the health of ethnic minorities living in its capital city, Lisbon. The Cape Verdean community in Lisbon tend to have low educational levels, material deprivation and struggle with discrimination and racism, factors that would probably be associated with a higher prevalence of overweight and obesity. Data for the Cape Verdean population were collected in three different time periods by three different research teams in 1993, 2009 and 2013 and included children aged 6–12 years living in the Cova da Moura neighbourhood of the Greater Lisbon Metro Area. The Portuguese national survey was conducted between 2009 and 2010 at public and private schools in mainland Portugal and included height, weight, skinfolds and arm and waist circumferences. From these survey data body mass index (BMI) and prevalence of stunting (chronic malnutrition – low height-for-age) and underweight (low weight-for-age) were calculated according to reference values proposed by Frisancho (2008). Overweight and obesity prevalence values were defined based on the references established by the International Obesity Task Force. The results show significant differences in height between Cape Verdean and Portuguese boys and girls. Generally, Cape Verdeans’ growth falls within the healthy range of international growth references across all of the survey data collected. Cape Verdean rates for combined overnutrition (overweight and obesity) in 2013 (9.8% for boys and 16.7% for girls) were lower than those of the Portuguese (33% for boys and 31.7% for girls). Logistic regression models showed that Cape Verdean children had a lower risk of being overweight or obese when accounting for breast-feeding, birth weight, maternal education and occupation. Despite living in a deprived neighbourhood these Cape Verdean children seemed to have grown more healthily than Portuguese ancestry children. The challenge for policymakers will be to support improvement of the poverty-related living conditions of this community without creating a risky environment for increasing prevalence of overweight and obesity.
Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption will generally be greater towards the entrance of a filter, where the concentration of contaminant particles is higher, these effects can also result in a spatially varying porosity. We investigate this dynamic process using an extension of homogenization theory that accounts for a macroscale variation in microstructure. We formulate and homogenize the coupled problems of flow through a filter with a near-periodic time-dependent microstructure, solute transport due to advection, diffusion and filter adsorption, and filter structure evolution due to the adsorption of contaminant. We use the homogenized equations to investigate how the contaminant removal and filter lifespan depend on the initial porosity distribution for a unidirectional flow. We confirm a conjecture made by Dalwadi et al. (Proc. R. Soc. Lond. A, vol. 471 (2182), 2015, 20150464) that filters with an initially negative porosity gradient have a longer lifespan and remove more contaminant than filters with an initially constant porosity, or worse, an initially positive porosity gradient. In addition, we determine which initial porosity distributions result in a filter that will block everywhere at once by exploiting an asymptotic reduction of the homogenized equations. We show that these filters remove more contaminant than other filters with the same initial average porosity, but that filters which block everywhere at once are limited by how large their initial average porosity can be.
We describe the performance of the Boolardy Engineering Test Array, the prototype for the Australian Square Kilometre Array Pathfinder telescope. Boolardy Engineering Test Array is the first aperture synthesis radio telescope to use phased array feed technology, giving it the ability to electronically form up to nine dual-polarisation beams. We report the methods developed for forming and measuring the beams, and the adaptations that have been made to the traditional calibration and imaging procedures in order to allow BETA to function as a multi-beam aperture synthesis telescope. We describe the commissioning of the instrument and present details of Boolardy Engineering Test Array’s performance: sensitivity, beam characteristics, polarimetric properties, and image quality. We summarise the astronomical science that it has produced and draw lessons from operating Boolardy Engineering Test Array that will be relevant to the commissioning and operation of the final Australian Square Kilometre Array Path telescope.
During 1990 we surveyed the southern sky using a multi-beam receiver at frequencies of 4850 and 843 MHz. The half-power beamwidths were 4 and 25 arcmin respectively. The finished surveys cover the declination range between +10 and −90 degrees declination, essentially complete in right ascension, an area of 7.30 steradians. Preliminary analysis of the 4850 MHz data indicates that we will achieve a five sigma flux density limit of about 30 mJy. We estimate that we will find between 80 000 and 90 000 new sources above this limit. This is a revised version of the paper presented at the Regional Meeting by the first four authors; the surveys now have been completed.
Thin glass sheets may be manufactured using a two-part process in which a sheet is first cast and then subsequently reheated and drawn to a required thickness. The latter redrawing process typically results in a sheet with non-uniform thickness and with smaller width than the cast glass block. Experiments suggest that the loss of width can be minimized and the non-uniformities can be essentially confined to thickening at the sheet edges if the heater zone through which the glass is drawn is made very short. We present a three-dimensional mathematical model for the redraw process and consider the limits in which (i) the heater zone is short compared with the sheet width, and (ii) the sheet thickness is small compared with both of these length scales. We show that, in the majority of the sheet, the properties vary only in the direction of drawing and the sheet motion is one-dimensional, with two-dimensional behaviour and the corresponding thick edges confined to boundary layers at the sheet extremities. We present numerical solutions to this boundary-layer problem and demonstrate good agreement with experiment, as well as with numerical solutions to the full three-dimensional problem. We show that the final thickness at the sheet edge scales with the inverse square root of the draw ratio, and explore the effect of tapering of the ends to identify a shape for the initial preform that results in a uniform rectangular final product.
Cognitive impairment in heart failure (HF) is believed to in part stem from structural brain alterations, including shrinkage of subcortical regions. Fortunately, neurocognitive dysfunction in HF can be mitigated by physical activity (PA), though mechanisms for this phenomenon are unclear. PA is protective against age-related cognitive decline that may involve improved structural integrity to brain regions sensitive to aging (e.g., subcortical structures). Yet, no study has examined the benefits of PA on the brain in HF and we sought to do so and clarify related cognitive implications. Fifty older adults with HF completed a neuropsychological battery and wore an accelerometer for 7 days. All participants underwent brain MRI. This study targeted subcortical brain volume given subcortical alterations are often observed in HF and the sensitivity of PA to subcortical structures in other patient populations. Participants averaged 4348.49 (SD=2092.08) steps per day and greater daily steps predicted better attention/executive function, episodic memory, and language abilities, p’s<.05. Medical and demographically adjusted regression analyses revealed higher daily steps per day predicted greater subcortical volume, with specific effects for the thalamus and ventral diencephalon, p’s<.05. Greater subcortical volume was associated with better attention/executive function, p<.05. Higher daily PA was associated with increased subcortical brain volume and better cognition in older adults with HF. Longitudinal work is needed to clarify whether daily PA can attenuate brain atrophy in HF to reduce accelerated cognitive decline in this population. (JINS, 2015, 21, 851–860)
In this paper, we consider the straining flow of a weakly interacting polymer–surfactant solution below a free surface, with the bulk surfactant concentration above the critical micelle concentration. We formulate a set of coupled differential equations describing the concentration of monomers, micelles, polymer, and polymer–micelle aggregates in the flow. We analyse the model in several asymptotic limits, and make predictions about the distribution of each of the species. In particular, in the large-reaction-rate limit we find that the model predicts a region near the free surface where no micelles or aggregates are present, and beneath this a region where the concentration of surfactant is constant, across which the concentration of aggregates increases until all the free polymer is consumed. For certain parameter regimes, a maximum in the concentration of the polymer–micelle complex occurs within the bulk fluid. In the finite-reaction-rate limit, micelles, and aggregates are present right up to the free surface, and the plateau in the concentration of surfactant in the bulk is no longer present. Results from the asymptotic theory compare favorably with full numerical solutions.
Canids, particularly dogs, constitute the major source of cystic echinococcosis (CE) infection to humans, with the majority of cases being caused by Echinococcus granulosus (G1 genotype). Canine echinococcosis is an asymptomatic disease caused by adult tapeworms of E. granulosus sensu lato (s.l.). Information on the population structure and genetic variation of adult E. granulosus is limited. Using sequenced data of the mitochondrial cytochrome c oxidase subunit 1 (cox1) we examined the genetic diversity and population structure of adult tapeworms of E. granulosus (G1 genotype) from canid definitive hosts originating from various geographical regions and compared it to that reported for the larval metacestode stage from sheep and human hosts. Echinococcus granulosus (s.s) was identified from adult tapeworm isolates from Kenya, Libya, Tunisia, Australia, China, Kazakhstan, United Kingdom and Peru, including the first known molecular confirmation from Gaza and the Falkland Islands. Haplotype analysis showed a star-shaped network with a centrally positioned common haplotype previously described for the metacestode stage from sheep and humans, and the neutrality indices indicated population expansion. Low Fst values suggested that populations of adult E. granulosus were not genetically differentiated. Haplotype and nucleotide diversities for E. granulosus isolates from sheep and human origin were twice as high as those reported from canid hosts. This may be related to self-fertilization of E. granulosus and/or to the longevity of the parasite in the respective intermediate and definitive hosts. Improved nuclear single loci are required to investigate the discrepancies in genetic variation seen in this study.
This paper describes the system architecture of a newly constructed radio telescope – the Boolardy engineering test array, which is a prototype of the Australian square kilometre array pathfinder telescope. Phased array feed technology is used to form multiple simultaneous beams per antenna, providing astronomers with unprecedented survey speed. The test array described here is a six-antenna interferometer, fitted with prototype signal processing hardware capable of forming at least nine dual-polarisation beams simultaneously, allowing several square degrees to be imaged in a single pointed observation. The main purpose of the test array is to develop beamforming and wide-field calibration methods for use with the full telescope, but it will also be capable of limited early science demonstrations.
We must begin with names. ‘Tony Edwards’ is the person to whom this volume is dedicated, but it is not a name that everyone will immediately recognize, particularly those who know him only from his published work, for he has made himself known in public, from the first, as A. S. G. Edwards. When he began his career, this was the manner in which most scholars, most men at least, named themselves. Fashions have changed, and given names, one, two, or more, are now almost universal. But Tony has held on tenaciously to his initials, perhaps because he has three of them. We do not believe that he did so in any spirit of emulation of or desire to align himself with ‘Edwards A. S. G.’, the Edwards Active Strain Gauge well known to Google, an advanced form of technical engineering equipment which guarantees the vacuum conditions needed for the manufacture of certain precision instruments, such as aircraft engine turbine blades. It seems strangely apt as an analogous form of ‘A. S. G.’, whether one thinks of the ‘active strain’ involved as what he exerts upon himself or upon other people. The analogy fails, of course, when one comes to the creation of vacuum, where it works back to front, for Tony's work has essentially been to fill the vacuum that once existed in the study of manuscript history.