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Thin, roughly horizontal low-permeability layers are a common form of large-scale heterogeneity in geological porous formations. In this paper, the dynamics of a buoyancy-driven plume in a two-dimensional layered porous medium is studied theoretically, with the aid of high-resolution numerical simulations. The medium is uniform apart from a thin, horizontal layer of a much lower permeability, located a dimensionless distance
below the dense plume source. If the dimensionless thickness
of the low-permeability layer are small, the effect of the layer is found to be well parameterized by its impedance
. Five different regimes of flow are identified and characterized. For
, the layer has no effect on the plume, but as
is increased the plume widens and spreads over the layer as a gravity current. For still larger
, the flow becomes destabilized by convective instabilities both below and above the layer, until, for
, the spread of the plume is dominated by convective mixing and buoyancy is transported across the layer by diffusion alone. Analytical models for the spread of the plume over the layer in the various different regimes are presented.
A significant percentage of the people outside their country of citizenship or residence who are unable to meet their basic needs on their own, and need international protection, do not fall under the definition set out in the UN Refugee Convention. This has led many – both academic commentators and activists – to call for a new, expanded refugee definition, preferably backed up by a new, binding, international convention. In earlier work, I have resisted this call, arguing that there is good reason to pick out a sub-set of those in need of international aid – a set that largely, if not completely, corresponds to those picked out by the Refugee Convention – for special benefit and protection. However, even if Convention refugees are in some ways special, we are left with the question of what, if anything, is owed to those in need of aid who are not Convention refugees. In this chapter, I set out philosophical foundations for so-called complementary protection.
This paper mounts a partial defense of the basic structure objection to the egalitarian criticism of productive incentives. The defense is based on the claim that some duties of justice are subject to a reciprocity condition. The paper develops this position via an examination of the debate between Andrew Williams and G. A. Cohen on publicity and incentives. Reciprocity is an intrinsic feature of a relational conception of social justice, not simply a requirement of stability. Not all duties are conditional on reciprocity because some duties are owed to third parties, as well as to their primary targets. Some forms of exploitation may be unconditionally wrong, but not the specific kind of exploitation at stake when talented individuals accept market wages.
The period before the formation of a persecutory delusion may provide causal insights. Patient accounts are invaluable in informing this understanding.
To inform the understanding of delusion formation, we asked patients about the occurrence of potential causal factors – identified from a cognitive model – before delusion onset.
A total of 100 patients with persecutory delusions completed a checklist about their subjective experiences in the weeks before belief onset. The checklist included items concerning worry, images, low self-esteem, poor sleep, mood dysregulation, dissociation, manic-type symptoms, aberrant salience, hallucinations, substance use and stressors. Time to reach certainty in the delusion was also assessed.
Most commonly it took patients several months to reach delusion certainty (n = 30), although other patients took a few weeks (n = 24), years (n = 21), knew instantly (n = 17) or took a few days (n = 6). The most frequent experiences occurring before delusion onset were: low self-confidence (n = 84); excessive worry (n = 80); not feeling like normal self (n = 77); difficulties concentrating (n = 77); going over problems again and again (n = 75); being very negative about the self (n = 75); images of bad things happening (n = 75); and sleep problems (n = 75). The average number of experiences occurring was high (mean 23.5, s.d. = 8.7). The experiences clustered into six main types, with patients reporting an average of 5.4 (s.d. = 1.0) different types.
Patients report numerous different experiences in the period before full persecutory delusion onset that could be contributory causal factors, consistent with a complex multifactorial view of delusion occurrence. This study, however, relied on retrospective self-report and could not determine causality.
We examine the motion in a shear flow at zero Reynolds number of particles with two planes of symmetry. We show that in most cases the rotational motion is qualitatively similar to that of a non-axisymmetric ellipsoid, and characterised by a combination of chaotic and quasiperiodic orbits. We use Kolmogorov–Arnold–Moser (KAM) theory and related ideas in dynamical systems to elucidate the underlying mathematical structure of the motion and thence to explain why such a large class of particles all rotate in essentially the same manner. Numerical simulations are presented for curved spheroids of varying centreline curvature, which are found to drift persistently across the streamlines of the flow for certain initial orientations. We explain the origin of this migration as the result of a lack of symmetries of the particle’s orientation orbit.
We consider peeling of an elastic sheet away from an elastic substrate through propagation of a fluid-filled crack along the interface between the two. The peeling is driven by a bending moment applied to the sheet and is resisted by viscous flow towards the crack tip and by the toughness of any bonding between the sheet and the substrate. Travelling-wave solutions are determined using lubrication theory coupled to the full equations of elasticity and fracture. The propagation speed
is the sheet’s thickness,
its plane-strain modulus,
the fluid viscosity,
the applied bending moment and
the sheet’s curvature due to bending; and the prefactor depends on the dimensionless toughness. If the toughness is small then there is a region of dry shear failure ahead of the fluid-filled region. The expressions for the propagation speed have been used to derive new similarity solutions for the spread of an axisymmetric fluid-filled blister in a variety of regimes: constant-flux injection resisted by elastohydrodynamics in the tip leads to spread proportional to
for peeling-by-bending, gravitational spreading and peeling-by-pulling, respectively.
The cognitive process of worry, which keeps negative thoughts in mind and elaborates the content, contributes to the occurrence of many mental health disorders. Our principal aim was to develop a straightforward measure of general problematic worry suitable for research and clinical treatment. Our secondary aim was to develop a measure of problematic worry specifically concerning paranoid fears.
An item pool concerning worry in the past month was evaluated in 250 non-clinical individuals and 50 patients with psychosis in a worry treatment trial. Exploratory factor analysis and item response theory (IRT) informed the selection of scale items. IRT analyses were repeated with the scales administered to 273 non-clinical individuals, 79 patients with psychosis and 93 patients with social anxiety disorder. Other clinical measures were administered to assess concurrent validity. Test-retest reliability was assessed with 75 participants. Sensitivity to change was assessed with 43 patients with psychosis.
A 10-item general worry scale (Dunn Worry Questionnaire; DWQ) and a five-item paranoia worry scale (Paranoia Worries Questionnaire; PWQ) were developed. All items were highly discriminative (DWQ a = 1.98–5.03; PWQ a = 4.10–10.7), indicating small increases in latent worry lead to a high probability of item endorsement. The DWQ was highly informative across a wide range of the worry distribution, whilst the PWQ had greatest precision at clinical levels of paranoia worry. The scales demonstrated excellent internal reliability, test-retest reliability, concurrent validity and sensitivity to change.
The new measures of general problematic worry and worry about paranoid fears have excellent psychometric properties.
We study the mechanisms affecting the viscous-fingering instability in an elastic-walled Hele-Shaw cell by considering the stability of steady states of unidirectional peeling-by-pulling and peeling-by-bending. We demonstrate that the elasticity of the wall influences the steady base state but has a negligible direct effect on the behaviour of linear perturbations, which thus behave like in the ‘printer’s instability’ with rigid walls. Moreover, the geometry of the cell can be very well approximated as a triangular wedge in the stability analysis. We identify four distinct mechanisms – surface tension acting on the horizontal and the vertical interfacial curvatures, kinematic compression in the longitudinal base flow, and the films deposited on the cell walls – that each contribute to stabilizing the system. The vertical curvature is the dominant stabilizing mechanism for small capillary numbers, but all four mechanisms have a significant effect in a large region of parameter space.
Excavations from 2013 to 2015 at the site of Shishan Marsh 1 (SM1) in the Azraq Basin of eastern Jordan have yielded substantial late middle Pleistocene lithic assemblages in association with faunal remains. Faunal preservation is poor, but multiple taxa have been identified, including cf. Panthera leo, Gazella sp., Bos cf. primigenius, Camelus sp., Equus spp., cf. Stephanorhinus hemitoechus, Palaeoloxodon cf. recki, and Elephas cf. hysudricus. The overall Azraq habitat may have been most similar to a savanna ecosystem, with a mixture of open grassland/shrub habitats and more closed vegetation along the wetlands margins. These taxa were drawn to the relatively lush oasis environment, where they were a dietary resource of the hominin groups exploiting the wetlands resources.
The flow of a viscous gravity current over a lubricating layer of fluid is modelled using lubrication theory. We study the case of an axisymmetric current with constant influx which allows for a similarity solution, which depends on three parameters: a non-dimensional influx rate
; a viscosity ratio
between the lower and upper layer fluid; and a relative density difference
. The limit of equal densities
is singular, as the interfacial evolution equation changes nature from parabolic to hyperbolic. Theoretical analysis of this limit reveals that a discontinuity, or shock, in the interfacial height forms above a critical viscosity ratio
, i.e. for a sufficiently less viscous upper-layer fluid. The physical mechanism for shock formation is described, which is based on advective steepening of the interface between the two fluids and relies on the lack of a contribution to the pressure gradient from the interfacial slope for equal-density fluids. In the limit of small but non-zero density differences, local travelling-wave solutions are found which regularise the singular structure of a potential shock and lead to a constraint on the possible shock heights in the form of an Oleinik entropy condition. Calculation of a simplified time-dependent system reveals the appropriate boundary conditions for the late-time similarity solution, which includes a shock at the nose of the current for
. The numerically calculated similarity solutions compare well to experimental measurements with respect to the predictions of self-similarity, the radial extent and the self-similar top-surface shapes of the current.
An assessment of topsoil (5–20cm) metal/metalloid (hereafter referred to as metal) concentrations across Glasgow and the Clyde Basin reveals that copper, molybdenum, nickel, lead, antimony and zinc show the greatest enrichment in urban versus rural topsoil (elevated 1.7–2.1 times; based on median values). This is a typical indicator suite of urban pollution also found in other cities. Similarly, arsenic, cadmium and lead are elevated 3.2–4.3 times the rural background concentrations in topsoil from the former Leadhills mining area. Moorlands show typical organic-soil geochemical signatures, with significantly lower (P<0.05) concentrations of geogenic elements such as chromium, copper, nickel, molybdenum and zinc, but higher levels of cadmium, lead and selenium than most other land uses due to atmospheric deposition/trapping of these substances in peat. In farmland, 14% of nickel and 7% of zinc in topsoil samples exceed agricultural maximum admissible concentrations, and may be sensitive to sewage-sludge application. Conversely, 5% of copper, 17% of selenium and 96% of pH in farmland topsoil samples are below recommended agricultural production thresholds. Significant proportions of topsoil samples exceed the most precautionary (residential/allotment) human-exposure soil guidelines for chromium (18% urban; 10% rural), lead (76% urban; 45% rural) and vanadium (87% urban; 56% rural). For chromium, this reflects volcanic bedrock and the history of chromite ore processing in the region. However, very few soil types are likely to exceed new chromiumVI-based guidelines. The number of topsoil samples exceeding the guidelines for lead and vanadium highlight the need for further investigations and evidence to improve human soil-exposure risk assessments to better inform land contamination policy and regeneration.
Geochemical and related studies have been made of near-surface sediments from the River Clyde estuary and adjoining areas, extending from Glasgow to the N, and W as far as the Holy Loch on the W coast of Scotland, UK. Multibeam echosounder, sidescan sonar and shallow seismic data, taken with core information, indicate that a shallow layer of modern sediment, often less than a metre thick, rests on earlier glacial and post-glacial sediments. The offshore Quaternary history can be aligned with onshore sequences, with the recognition of buried drumlins, settlement of muds from quieter water, probably behind an ice dam, and later tidal delta deposits. The geochemistry of contaminants within the cores also indicates shallow contaminated sediments, often resting on pristine pre-industrial deposits at depths less than 1m. The distribution of different contaminants with depth in the sediment, such as Pb (and Pb isotopes), organics and radionuclides, allow chronologies of contamination from different sources to be suggested. Dating was also attempted using microfossils, radiocarbon and 210Pb, but with limited success. Some of the spatial distribution of contaminants in the surface sediments can be related to grain-size variations. Contaminants are highest, both in absolute terms and in enrichment relative to the natural background, in the urban and inner estuary and in the Holy Loch, reflecting the concentration of industrial activity.
We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet. The introduction of wall elasticity delays the onset of the fingering instability to much larger values of the injection flow rate. Furthermore, when the instability develops, the fingers that form on the expanding air–liquid interface are short and stubby, in contrast with the highly branched patterns observed in rigid-walled cells (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108, 2012, 074502). We report the outcome of a comprehensive experimental study of this problem and compare the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Föppl–von-Kármán equations which describe the deformation of the elastic sheet. We perform a linear stability analysis to study the evolution of small-amplitude non-axisymmetric perturbations to the time-evolving base flow. We then derive a simplified model by exploiting the observations (i) that the non-axisymmetric perturbations to the sheet are very small and (ii) that perturbations to the flow occur predominantly in a small wedge-shaped region ahead of the air–liquid interface. This allows us to identify the various physical mechanisms by which viscous fingering is weakened (or even suppressed) by the presence of wall elasticity. We show that the theoretical predictions for the growth rate of small-amplitude perturbations are in good agreement with experimental observations for injection flow rates that are slightly larger than the critical flow rate required for the onset of the instability. We also characterize the large-amplitude fingering patterns that develop at larger injection flow rates. We show that the wavenumber of these patterns is still well predicted by the linear stability analysis, and that the length of the fingers is set by the local geometry of the compliant cell.
Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.
The SKA and its pathfinders will enable studies of H i emission at higher redshifts than ever before. In moving beyond the local Universe, this will require the use of cosmologically appropriate formulae that have traditionally been simplified to their low-redshift approximations. In this paper, we summarise some of the most important relations for tracing H i emission in the SKA era, and present an online calculator to assist in the planning and analysis of observations (http://hifi.icrar.org).
The stability of steady convective exchange flow with a rectangular planform in an unbounded three-dimensional porous medium is explored. The base flow comprises a balance between vertical advection with amplitude
in interleaving rectangular columns with aspect ratio
and horizontal diffusion between the columns. Columnar flow with a square planform (
) is found to be weakly unstable to a large-scale perturbation of the background temperature gradient, irrespective of
, but to have no stronger instability on the scale of the columns. This result provides a stark contrast to two-dimensional columnar flow (Hewitt et al., J. Fluid Mech., vol. 737, 2013, pp. 205–231), which, as
is increased, is increasingly unstable to a perturbation on the scale of the columnar wavelength. For rectangular planforms with
, a critical aspect ratio is identified, below which a perturbation on the scale of the columns is the fastest growing mode, as in two dimensions. Scalings for the growth rate and the structure of this mode are identified, and are explained by means of an asymptotic expansion in the limit
. The difference between the stabilities of two-dimensional and three-dimensional exchange flow provides a potential explanation for the apparent difference in dominant horizontal scale observed in direct numerical simulations of two-dimensional and three-dimensional statistically steady ‘Rayleigh–Darcy’ convection at high Rayleigh numbers.
The equilibration time
in response to a change in flux from
after an injection period
applied to either a low-Reynolds-number gravity current or one propagating through a porous medium, in both axisymmetric and one-dimensional geometries, is shown to be of the form
, independent of all the remaining physical parameters. Numerical solutions are used to investigate
for each of these situations and compare very well with experimental results in the case of an axisymmetric current propagating over a rigid horizontal boundary. Analysis of the relaxation towards self-similarity provides an illuminating connection between the excess (deficit) volume from early times and an asymptotically equivalent shift in time origin, and hence a good quantitative estimate of
. The case
of equilibration after ceasing injection at time
is a singular limit. Extensions to high-Reynolds-number currents and to the case of a constant-volume release followed by constant-flux injection are discussed briefly.