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A reduced model is presented for the dynamics of a slender sheet of a viscoelastic fluid. Starting with the Oldroyd-B constitutive model and exploiting an asymptotic analysis in the small aspect ratio of the sheet, equations are derived for the evolution of a ‘visco-elastica’. These depend on an elastic modulus, a creep viscosity and a solvent viscosity. They resemble standard equations for an elastica or a viscida, to which they reduce under the appropriate limits. The model is used to explore the effects of viscoelasticity on the dynamics of a curling ribbon, a drooping cantilever, buckling sheets, snap-through and a falling catenary. We then incorporate a yield stress, for a fluid that deforms by creep only above a critical stress, revisiting the curling and cantilever problems. This model generalises a number of previous theories for viscoelastic and viscoplastic ribbons.
Three related problems of viscoplastic flow around cylinders are considered. First, translating cylinders with no-slip surfaces appear to generate adjacent rotating plugs in the limit where the translation speed becomes vanishingly small. In this plastic limit, analytical results are available from plasticity theory (slipline theory) which indicate that no such plugs should exist. Using a combination of numerical computations and asymptotic analysis, we show that the plugs of the viscoplastic theory actually disappear in the plastic limit, albeit very slowly. Second, when the boundary condition on the cylinder is replaced by one that permits sliding, the plastic limit corresponds to a partially rough cylinder. In this case, no plasticity solution has been previously established; we provide evidence from numerical computations and slipline theory that a previously proposed upper bound (Martin & Randolph, Geotechnique, vol. 56, 2006, pp. 141–145) is actually the true plastic solution. Third, we consider how a prescribed surface velocity field can propel cylindrical squirmers through a viscoplastic fluid. We determine swimming speeds and contrast the results with those from the corresponding Newtonian problem.
The theory of slow viscous flow around a slender body is generalized to the situation where the ambient fluid has a yield stress. The local flow around a cylinder that is moving along or perpendicular to its axis, and rotating, provides a first step in this theory. Unlike for a Newtonian fluid, the nonlinearity associated with the viscoplastic constitutive law precludes one from linearly superposing solutions corresponding to each independent component of motion, and instead demands a full numerical approach to the problem. This is accomplished for the case of a Bingham fluid, along with a consideration of some asymptotic limits in which analytical progress is possible. Since the yield stress of the fluid strongly localizes the flow around the body, the leading-order slender-body approximation is rendered significantly more accurate than the equivalent Newtonian problem. The theory is applied to the sedimentation of inclined cylinders, bent rods and helices, and compared with some experimental data. Finally, the theory is applied to the locomotion of a cylindrical filament driven by helical waves through a viscoplastic fluid.
A yield stress is added to Taylor’s (Proc. R. Soc. Lond. A, vol. 209, 1951, pp. 447–461) model of a two-dimensional flexible sheet swimming through a viscous fluid. Both transverse waves along the sheet, as in Taylor’s original model, and longitudinal waves are considered as means of locomotion. In each case, numerical solutions are provided over a range of the two key parameters of the problem: the wave amplitude relative to the wavelength and a Bingham number which describes the strength of the yield stress. The numerical solutions are supplemented with discussions of various limits of the problem in which analytical progress is possible. When the yield stress is large, the swimming speed for low wave amplitude is exactly double that for a Newtonian fluid, for either type of wave.
In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplastic flows can develop narrow boundary layers that provide either surfaces of failure between rigid plugs, the lubrication between a plugged flow and a wall or buffers for regions of predominantly plastic deformation. Oldroyd (Proc. Camb. Phil. Soc., vol. 43, 1947, pp. 383–395) presented the first theoretical discussion of these viscoplastic boundary layers, offering an asymptotic reduction of the governing equations and a discussion of some model flow problems. However, the complicated nonlinear form of Oldroyd’s boundary-layer equations has evidently precluded further discussion of them. In the current paper, we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples of a jet-like intrusion and flow past a thin plate. We also consider flow down channels with either sudden expansions or wavy walls. In all these examples, we verify that viscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extract the dependence of the boundary-layer thickness and flow profiles on the dimensionless yield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layer theory applies to free viscoplastic shear layers, it does not apply when the boundary layer is adjacent to a wall, as has been observed previously for two-dimensional flow around circular obstructions. Instead, the boundary-layer thickness scales in a different fashion with the Bingham number, as suggested by classical solutions for plane-parallel flows, lubrication theory and, for flow around a plate, by Piau (J. Non-Newtonian Fluid Mech., vol. 102, 2002, pp. 193–218); we rationalize this second scaling and provide an alternative boundary-layer theory.
Over 300 cases of acute toxoplasmosis are confirmed by reference testing in England and Wales annually. We conducted a case-control study to identify risk factors for Toxoplasma gondii infection to inform prevention strategies. Twenty-eight cases and 27 seronegative controls participated. We compared their food history and environmental exposures using logistic regression to calculate odds ratios (OR) and 95% confidence intervals in a model controlling for age and sex. Univariable analysis showed that the odds of eating beef (OR 10·7, P < 0·001), poultry (OR 6·4, P = 0·01) or lamb/mutton (OR 4·9, P = 0·01) was higher for cases than controls. After adjustment for potential confounders a strong association between beef and infection remained (OR 5·6, P = 0·01). The small sample size was a significant limitation and larger studies are needed to fully investigate potential risk factors. The study findings emphasize the need to ensure food is thoroughly cooked and handled hygienically, especially for those in vulnerable groups.
A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with stepwise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interference of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow.
The Murchison Widefield Array is a Square Kilometre Array Precursor. The telescope is located at the Murchison Radio–astronomy Observatory in Western Australia. The MWA consists of 4 096 dipoles arranged into 128 dual polarisation aperture arrays forming a connected element interferometer that cross-correlates signals from all 256 inputs. A hybrid approach to the correlation task is employed, with some processing stages being performed by bespoke hardware, based on Field Programmable Gate Arrays, and others by Graphics Processing Units housed in general purpose rack mounted servers. The correlation capability required is approximately 8 tera floating point operations per second. The MWA has commenced operations and the correlator is generating 8.3 TB day−1 of correlation products, that are subsequently transferred 700 km from the MRO to Perth (WA) in real-time for storage and offline processing. In this paper, we outline the correlator design, signal path, and processing elements and present the data format for the internal and external interfaces.
The Murchison Widefield Array is a new low-frequency interferometric radio telescope built in Western Australia at one of the locations of the future Square Kilometre Array. We describe the automated radio-frequency interference detection strategy implemented for the Murchison Widefield Array, which is based on the aoflagger platform, and present 72–231 MHz radio-frequency interference statistics from 10 observing nights. Radio-frequency interference detection removes 1.1% of the data. Radio-frequency interference from digital TV is observed 3% of the time due to occasional ionospheric or atmospheric propagation. After radio-frequency interference detection and excision, almost all data can be calibrated and imaged without further radio-frequency interference mitigation efforts, including observations within the FM and digital TV bands. The results are compared to a previously published Low-Frequency Array radio-frequency interference survey. The remote location of the Murchison Widefield Array results in a substantially cleaner radio-frequency interference environment compared to Low-Frequency Array’s radio environment, but adequate detection of radio-frequency interference is still required before data can be analysed. We include specific recommendations designed to make the Square Kilometre Array more robust to radio-frequency interference, including: the availability of sufficient computing power for radio-frequency interference detection; accounting for radio-frequency interference in the receiver design; a smooth band-pass response; and the capability of radio-frequency interference detection at high time and frequency resolution (second and kHz-scale respectively).
We consider a nonlinear diffusion equation describing the planar spreading of a viscous fluid injected between an elastic sheet and an underlying rigid plane. The dynamics depends sensitively on the physical conditions at the contact line where the sheet is lifted off the plane by the fluid. We explore two possibilities for these conditions (or “regularisations”): a pre-wetted film and a constant-pressure fluid lag (a gas-filled gap between the fluid edge and the contact line). For both flat and inclined planes, we compare numerical and asymptotic solutions, identifying the distinct stages of evolution and the corresponding characteristic rates of spreading.
Significant new opportunities for astrophysics and cosmology have been identified at low radio frequencies. The Murchison Widefield Array is the first telescope in the southern hemisphere designed specifically to explore the low-frequency astronomical sky between 80 and 300 MHz with arcminute angular resolution and high survey efficiency. The telescope will enable new advances along four key science themes, including searching for redshifted 21-cm emission from the EoR in the early Universe; Galactic and extragalactic all-sky southern hemisphere surveys; time-domain astrophysics; and solar, heliospheric, and ionospheric science and space weather. The Murchison Widefield Array is located in Western Australia at the site of the planned Square Kilometre Array (SKA) low-band telescope and is the only low-frequency SKA precursor facility. In this paper, we review the performance properties of the Murchison Widefield Array and describe its primary scientific objectives.
Multiple norovirus outbreaks following catered events in Auckland, New Zealand, in September 2010 were linked to the same catering company and investigated. Retrospective cohort studies were undertaken with attendees of two events: 38 (24·1%) of 158 surveyed attendees developed norovirus-compatible illness. Attendees were at increased risk of illness if they had consumed food that had received manual preparation following cooking or that had been prepared within 45 h following end of symptoms in a food handler with prior gastroenteritis. All food handlers were tested for norovirus. A recombinant norovirus GII.e/GII.4 was detected in specimens from event attendees and the convalescent food handler. All catering company staff were tested; no asymptomatic norovirus carriers were detected. This investigation improved the characterization of norovirus risk from post-symptomatic food handlers by narrowing the potential source of transmission to one individual. Food handlers with gastroenteritis should be excluded from the workplace for 45 h following resolution of symptoms.
The Murchison Widefield Array (MWA) is one of three Square Kilometre Array Precursor telescopes and is located at the Murchison Radio-astronomy Observatory in the Murchison Shire of the mid-west of Western Australia, a location chosen for its extremely low levels of radio frequency interference. The MWA operates at low radio frequencies, 80–300 MHz, with a processed bandwidth of 30.72 MHz for both linear polarisations, and consists of 128 aperture arrays (known as tiles) distributed over a ~3-km diameter area. Novel hybrid hardware/software correlation and a real-time imaging and calibration systems comprise the MWA signal processing backend. In this paper, the as-built MWA is described both at a system and sub-system level, the expected performance of the array is presented, and the science goals of the instrument are summarised.
We investigate the dynamics of an object towed over the surface of an initially flat, deformable layer. Using a combination of simple laboratory experiments and a theoretical model, we demonstrate that an inclined plate, pivoted so as to move up and down, may be towed steadily over a substrate at low speed, but become unstable to vertical oscillations above a threshold speed. That threshold depends upon the weight of the plate and the physical properties of the substrate, but arises whether the substrate is a viscous fluid, a viscoplastic fluid, or a granular medium. For the latter two materials, the unstable oscillations imprint a permanent rippled pattern on the layer, suggesting that the phenomenon of the ‘washboard road’ can arise from the passage of a single vehicle (i.e. the absolute instability of a flat bed). We argue that the mechanism behind the instability originates from the mound of material that is pushed forward ahead of the object: the extent of the mound determines the resultant force, whereas its growth is controlled by the object’s height relative to the undisturbed surface, allowing for an unstable coupling between the vertical motion and the substrate deformation.
Using a combination of theoretical modelling and experiments, seiches in a reservoir are shown to become linearly unstable due to the coupling with flow under a dam that opens and closes in response to the upstream water pressure. The phenomenon is related to the mechanism commonly attributed to generate sound in musical instruments like the clarinet. Shallow water theory is used to model waves in the reservoir, and these are coupled, by an outflow condition, to a nonlinear oscillator equation for the dam opening. In general, several modes of oscillation are predicted to be unstable, and the frequency of the most unstable mode compares well with the dominant frequencies observed in the experiments. The experiments also show a systematic variation of the amplitude and spatial structure of the oscillations with the weight of the dam, reflecting the nonlinear coupling between the unstable modes of the system.
Experiments are conducted to study the planing and skipping of a rectangular paddle on the surface of a shallow stream. The paddle is allowed to move freely up and down by attaching it to a pivoted arm. A steady planing state, in which the lift force from the water balances the weight on the paddle, is found to be stable for small stream velocities but to become unstable above a certain threshold velocity which depends upon the weight and the angle of attack. Above this threshold, the paddle oscillates in the water and can take off into a continual bouncing, or skipping, motion, with a well-defined amplitude and frequency. The transition is sometimes bistable so that both a steady planing state and a regular skipping state are possible for the same experimental parameters. Shallow-water theory is used to construct simple models that explain the qualitative features of the planing and skipping states in the experiments. It is found that a simple parameterisation of the lift force on the paddle proportional to the depth of entry is not sufficient to explain the observations, and it is concluded that the rise of water ahead of the paddle, in particular the way this varies over time, is responsible for causing the planing state to become unstable and for enabling a continual skipping state.
Five large outbreaks of food poisoning are described in which clinical, epidemiological or laboratory data indicated Clostridium perfringens as the causative organism. The foodstuff common to all incidents was boiled salmon served cold as an hors d'oeuvre. In all cases the fish had been subject to a long period of cooling or storage between boiling and consumption. It is thought that multiplication of the organism occurred during this time.
Recommendations are made for the avoidance of further similar incidents.
Bacteria and yeasts have been the organisms of choice for the industrial production of heterologous recombinant proteins for many years. The ability to cultivate bacterial strains to high cell density at large scale has become an increasingly important technique throughout the field of biotechnology, from basic research programmes (structural or kinetic studies) to large-scale pharmaceutical production processes. Escherichia coli remains one of the most attractive organisms for the production of recombinant proteins (see Chapters 4, 5, and 21 for examples) where no complex post-translational modifications (e.g. glycosylation or disulphide bond formation) are required for biological activity and because its genetics and physiology are well understood. However, there are important drawbacks associated with the use of prokaryotic organisms. The low percentage of GC nucleotides in their genomes, when compared to mammalian genes, and the existence of rare codons that often result in low expression levels or inactive truncated forms and, in many cases, proteins are expressed as insoluble inclusion bodies in the bacterial periplasmic space. Bacteria are also incapable of carrying out any post-translational modifications, which strongly influences protein stability, folding, solubility and, hence, its biological activity. Yeasts (e.g. Saccaromyces cerevisiae or Pichia pastoris), though, can perform some post-translational modifications similar to those of the more complex eukaryotic cells (see Chapter 5). However N-glycosylation of mammalian proteins in yeast seems to be very inefficient. Additionally, both bacteria and yeast cells are surrounded by a mechanically strong cell wall that may hinder recovery of any non-secreted proteins.
Dissipative heating is produced by irreversible processes, such as viscous or ohmic heating, in a convecting fluid; its importance depends on the ratio d/HT of the depth of the convecting region to the temperature scale height. Integrating the entropy equation for steady flow yields an upper bound to the total rate of dissipative heating in a convecting layer. For liquids there is a regime in which the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number. This result is confirmed by numerical experiments using the Boussinesq approximation, which is valid only if d/HT is small. For deep layers the dissipative heating rate may be much greater than the convected heat flux. If the earth's magnetic field is maintained by a convectively driven dynamo, ohmic losses are limited to 5% of the convected flux emerging from the core. In the earth's mantle viscous heating may be important locally beneath ridges and behind island arcs.