A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

A thin rivulet or ridge subject to a uniform transverse\ud shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

Identification and characterisation of 17 polymorphic candidate genes for response to parasitic nematode (Trichostrongylus tenuis) infection in red grouse (Lagopus lagopus scotica)

Acknowledgements This study was funded by a BBSRC studentship (MA Wenzel) and NERC Grants NE/H00775X/1 and NE/D000602/1 (SB Piertney). We are grateful to Jacob Hoglund for providing willow grouse samples, Mario Roder, Keliya Bai, Marianne James, Matt Oliver, Gill Murray-Dickson, Francois Mougeot and Jesus Martınez-Padilla for help with fieldwork, and all grouse estate factors, owners and keepers, most particularly Alistair Mitchell, Shaila Rao, Christopher Murphy, Richard Cooke and Fred Taylor, for providing access to estate game larders.Peer reviewedPostprin

Workshop on the Polar Regions of Mars: Geology, Glaciology, and Climate History, part 1

Papers and abstract of papers presented at the workshop are presented. Some representative titles are as follows: Glaciation in Elysium; Orbital, rotational, and climatic interactions; Water on Mars; Rheology of water-silicate mixtures at low temperatures; Evolution of the Martian atmosphere (the role of polar caps); Is CO2 ice permanent; Dust transport into Martian polar latitudes; Mars observer radio science (MORS) observations in polar regions; and Wind transport near the poles of Mars (timescales of changes in deposition and erosion)

A geometric view of cryptographic equation solving

This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods

A transcriptomic investigation of handicap models in sexual selection

We are grateful to D. Calder and T. Helps for access to study sites, and G. Murray-Dickson and M. Oliver for help with fieldwork and comments on manuscript drafts. This work was funded by NERC grant NE/D000602/1 (SBP), a NERC advanced fellowship (FM) and a BBSRC studentship (MAW)Peer reviewedPostprin

Outbreak of encephalitic listeriosis in red-legged partridges (Alectoris rufa)

An outbreak of neurological disease was investigated in red-legged partridges between 8 and 28 days of age. Clinical signs included torticollis, head tilt and incoordination and over an initial eight day period approximately 30–40 fatalities occurred per day. No significant gross post mortem findings were detected. Histopathological examination of the brain and bacterial cultures followed by partial sequencing confirmed a diagnosis of encephalitis due to Listeria monocytogenes. Further isolates were obtained from follow-up carcasses, environmental samples and pooled tissue samples of newly imported day-old chicks prior to placement on farm. These isolates had the same antibiotic resistance pattern as the isolate of the initial post mortem submission and belonged to the same fluorescent amplified fragment length polymorphism (fAFLP) subtype. This suggested that the isolates were very closely related or identical and that the pathogen had entered the farm with the imported day-old chicks, resulting in disease manifestation in partridges between 8 and 28 days of age. Reports of outbreaks of encephalitic listeriosis in avian species are rare and this is to the best of our knowledge the first reported outbreak in red-legged partridges