Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

Transport and distribution of lindane and simazine in a riverine environment: measurements in bed sediments and modelling

Aquatic sediments often remove hydrophobic contaminants from fresh waters. The subsequent distribution and concentration of contaminants in bed sediments determines their effect on benthic organisms and the risk of re-entry into the water and/or leaching to groundwater. This study examines the transport of simazine and lindane in aquatic bed sediments with the aim of understanding the processes that determine their depth distribution. Experiments in flume channels (water flow of 10 cm s(-1)) determined the persistence of the compounds in the absence of sediment with (a) de-ionised water and (b) a solution that had been in contact with river sediment. In further experiments with river bed sediments in light and dark conditions, measurements were made of the concentration of the compounds in the overlying water and the development of bacterial/algal biofilms and bioturbation activity. At the end of the experiments, concentrations in sediments and associated pore waters were determined in sections of the sediment at 1 mm resolution down to 5 mm and then at 10 mm resolution to 50 mm depth and these distributions analysed using a sorption-diffusion-degradation model. The fine resolution in the depth profile permitted the detection of a maximum in the concentration of the compounds in the pore water near the surface, whereas concentrations in the sediment increased to a maximum at the surface itself. Experimental distribution coefficients determined from the pore water and sediment concentrations indicated a gradient with depth that was partly explained by an increase in organic matter content and specific surface area of the solids near the interface. The modelling showed that degradation of lindane within the sediment was necessary to explain the concentration profiles, with the optimum agreement between the measured and theoretical profiles obtained with differential degradation in the oxic and anoxic zones. The compounds penetrated to a depth of 40-50 rum over a period of 42 days. (C) 2004 Society of Chemical Industry.

Diffusion of the synthetic pyrethroid permethrin into bed-sediments

Bed-sediments are a sink for many micro-organic contaminants in aquatic environments. The impact of toxic contaminants on benthic fauna often depends on their spatial distribution, and the fate of the parent compounds and their metabolites. The distribution of a synthetic pyrethroid, permethrin, a compound known to be toxic to aquatic invertebrates, was studied using river bed-sediments in lotic flume channels. trans/cis-Permethrin diagnostic ratios were used to quantify the photoisomerization of the trans isomer in water. Rates were affected by the presence of sediment particles and colloids when compared to distilled water alone. Two experiments in dark/light conditions with replicate channels were undertaken using natural sediment, previously contaminated with permethrin, to examine the effect of the growth of an algal biofilm at the sediment-water interface on diffusive fluxes of permethrin into the sediment. After 42 days, the bulk water was removed, allowing a fine sectioning of the sediment bed (i.e., every mm down to 5 mm and then 5-10 mm, then every 10 mm down to 50 mm). Permethrin was detected in all cases down to a depth of 5-10 mm, in agreement with estimates by the Millington and Quirk model, and measurements of concentrations in pore water produced a distribution coefficient (K-d) for each section, High K-d's were observed for the top layers, mainly as a result of high organic matter and specific surface area. Concentrations in the algal biofilm measured at the end of the experiment under light conditions, and increases in concentration in the top 1 mm of the sediment, demonstrated that algal/bacterial biofilm material was responsible for high K-d's at the sediment surface, and for the retardation of permethrin diffusion. This specific partition of permethrin to fine sediment particles and algae may enhance its threat to benthic invertebrates. In addition,the analysis of trans/cis-permethrin isomer ratios in sediment showed greater losses of trans-permethrin in the experiment under light conditions, which may have also resulted from enhanced biological activity at the sediment surface.

An ichnofabric approach to the depositional interpretation of the intensely burrowed Bateig Limestone, Miocene, SE Spain

The foraminiferal-rich pelagic Bateig Limestone forms several varieties of the important building stones quarried at Bateig Hill in southeastern Spain. Three principal ichnofabrics (Bichordites, mottled-Palaeophycus and mottled-Ophiomorpha) are recognized, which are present in at least two (possibly up to four) repeated successions (cycles). Each succession begins with an erosional event. The Bichordites ichnofabric represents a new type of facies, formed as thin turbidity/grain flow, stratiform units derived from sediment slips off a fault into deep water. Each slipped unit became almost completely bioturbated by infaunal echinoids, colonizing by lateral migration. Because of the thinness of the units, successive colonizations tended to truncate the underlying burrows giving rise to a pseudo-stratification. As the Bichordites ichnofabric accumulated on the fault apron, thus reducing the effective height of the fault scarp, the substrate gradually came under the influence of currents traversing the shelf. This led to a change in hydraulic regime, and to the mottled-Palaeophycus and mottled-Ophiomorpha ichnofabrics in sediment deposited under bed load transport, and associated with laminar and cross-stratified beds and local muddy intervals. Reactivation of the fault triggered erosion and channeling and a return to grain flow sedimentation, and to the Bichordites ichnofabric of the succeeding cycle. The highest unit of the Bateig Limestone is formed entirely of cross-stratified calcarenites with occasional Ophiomorpha (Ophiomorpha-primary lamination ichnofabric) and is similar to many shallow marine facies but they still bear a significant content of pelagic foraminifera. The sedimentary setting bears resemblance with that described for the Pleistocene Monte Torre Paleostrait and the modem Strait of Messina (Italy), where the narrow morphology of the depositional area enhanced tidal currents and allowed for high-energy sandy deposition in relatively deep areas. More data on the Miocene paleogeography of the Bateig area should provide further testing for this hypothesis. The ichnofacies and stacking of the Bateig Limestone differ from the classic Seilacherian model in that they reflect changes in hydraulic process and are associated with faulting and subsidence and changes in sediment supply. Recognition of the unusual ichnofabrics and their relationships provides a clear indication of the overall dynamic setting. (c) 2006 Elsevier B.V. All rights reserved.

Joined-up archaeology at Old Scatness, Shetland: thin section analysis of the site and hinterland

Excavations on the multi-period settlement at Old Scatness, Shetland have uncovered a number of Iron Age structures with compacted, floor-like layers. Thin section analysis was undertaken in order to investigate and compare the characteristics of these layers. The investigation also draws on earlier analyses of the Iron Age agricultural soil around the settlement and the midden deposits that accumulated within the settlement, to create a 'joined-up' analysis which considers the way material from the settlement was used and then recycled as fertiliser for the fields. Peat was collected from the nearby uplands and was used for fuel and possibly also for flooring. It is suggested that organic-rich floors from the structures were periodically removed and the material was spread onto the fields as fertilisers. More organic-rich material may have been used selectively for fertiliser, while the less organic peat ash was allowed to accumulate in middens. Several of the structures may have functioned as byres, which suggests a prehistoric plaggen system.

Geomorphological Map of Ribbed Moraines on the Dubawnt Lake Palaeo-Ice Stream Bed: A Signature of Ice Stream Shut-down?

The beds of active ice streams in Greenland and Antarctica are largely inaccessible, hindering a full understanding of the processes that initiate, sustain and inhibit fast ice flow in ice sheets. Detailed mapping of the glacial geomorphology of palaeo-ice stream tracks is, therefore, a valuable tool for exploring the basal processes that control their behaviour. In this paper we present a map that shows detailed glacial geomorphology from a part of the Dubawnt Lake Palaeo-Ice Stream bed on the north-western Canadian Shield (Northwest Territories), which operated at the end of the last glacial cycle. The map (centred on 63 degrees 55 '' 42'N, 102 degrees 29 '' 11'W, approximate scale 1:90,000) was compiled from digital Landsat Enhanced Thematic Mapper Plus satellite imagery and digital and hard-copy stereo-aerial photographs. The ice stream bed is dominated by parallel mega-scale glacial lineations (MGSL), whose lengths exceed several kilometres but the map also reveals that they have, in places, been superimposed with transverse ridges known as ribbed moraines. The ribbed moraines lie on top of the MSGL and appear to have segmented the individual lineaments. This indicates that formation of the ribbed moraines post-date the formation of the MSGL. The presence of ribbed moraine in the onset zone of another palaeo-ice stream has been linked to oscillations between cold and warm-based ice and/or a patchwork of cold-based areas which led to acceleration and deceleration of ice velocity. Our hypothesis is that the ribbed moraines on the Dubawnt Lake Ice Stream bed are a manifestation of the process that led to ice stream shut-down and may be associated with the process of basal freeze-on. The precise formation of ribbed moraines, however, remains open to debate and field observation of their structure will provide valuable data for formal testing of models of their formation.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Multi-mode approximations to wave scattering by an uneven bed

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are Investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

The sediment trapping efficiency of the macro-tidal Daly Estuary, tropical Australia

Field studies were carried out on the water and sediment dynamics in the tropical, macro-tidal, Daly Estuary. The estuary is shallow, very-turbid, about 100 km long, and the entrance is funnel-shape. In the wet, high flow season, normal tidal ranges can be suppressed in the estuary, depending on inflow rates, and freshwater becomes dominant up to the mouth. At that time a fraction of the fine sediment load is exported offshore as a bottom-tagging nepheloid layer after the sediment falls out of suspension of the thin, near-surface, river plume. The remaining fraction and the riverine coarse sediment form a large sediment bar 10 km long, up to 6 m in height and extending across the whole width of the channel near the mouth. This bar, as well as shoals in the estuary, partially pond the mid- to upper-estuary. This bar builds up from the deposition of riverine sediment during a wet season with high runoff and can raise mean water level by up to 2 m in the upper estuary in the low flow season. This ponding effect takes about three successive dry years to disappear by the sediment forming the bar being redistributed all over the estuary by tidal pumping of fine and coarse sediment in the dry season, which is the low flow season. The swift reversal of the tidal currents from ebb to flood results in macro-turbulence that lasts about 20 min. Bed load transport is preferentially landward and occurs only for water currents greater than 0.6 m s(-1). This high value of the threshold velocity suggests that the sand may be cemented by the mud. The Daly Estuary thus is a leaky sediment trap with an efficiency varying both seasonally and inter-annually. (c) 2006 Elsevier Ltd. All rights reserved.