Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Electron beam current loss at the high-vacuum-high-pressure boundary in the environmental scanning electron microscope

A significant loss in electron probe current can occur before the electron beam enters the specimen chamber of an environmental scanning electron microscope (ESEM). This loss results from electron scattering in a gaseous jet formed inside and downstream (above) the pressure-limiting aperture (PLA), which separates the high-pressure and high-vacuum regions of the microscope. The electron beam loss above the PLA has been calculated for three different ESEMs, each with a different PLA geometry: an ElectroScan E3, a Philips XL30 ESEM, and a prototype instrument. The mass thickness of gas above the PLA in each case has been determined by Monte Carlo simulation of the gas density variation in the gas jet. It has been found that the PLA configurations used in the commercial instruments produce considerable loss in the electron probe current that dramatically degrades their performance at high chamber pressure and low accelerating voltage. These detrimental effects are minimized in the prototype instrument, which has an optimized thin-foil PLA design.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Orbitally induced oscillations in the East Antarctic ice sheet at the Oligocene/Miocene boundary

Between 34 and 15 million years (Myr) ago, when planetary temperatures were 3-4 degreesC warmer than at present and atmospheric CO2 concentrations were twice as high as today(1), the Antarctic ice sheets may have been unstable(2-7). Oxygen isotope records from deep-sea sediment cores suggest that during this time fluctuations in global temperatures and high-latitude continental ice volumes were influenced by orbital cycles(8-10). But it has hitherto not been possible to calibrate the inferred changes in ice volume with direct evidence for oscillations of the Antarctic ice sheets(11). Here we present sediment data from shallow marine cores in the western Ross Sea that exhibit well dated cyclic variations, and which link the extent of the East Antarctic ice sheet directly to orbital cycles during the Oligocene/Miocene transition (24.1-23.7 Myr ago). Three rapidly deposited glaci-marine sequences are constrained to a period of less than 450 kyr by our age model, suggesting that orbital influences at the frequencies of obliquity (40 kyr) and eccentricity (125 kyr) controlled the oscillations of the ice margin at that time. An erosional hiatus covering 250 kyr provides direct evidence for a major episode of global cooling and ice-sheet expansion about 23.7 Myr ago, which had previously been inferred from oxygen isotope data (Mil event(5)).

Smoke derived from burnt vegetation stimulates germination of arable weeds

A commercially available smoke-water solution (Seed Starter (R)) stimulated the germination of caryopses and intact florets of Avena fatua L. The solution was most effective when diluted (5-50%) and presented to intact or dehulled grain that had received a short period of dry after-ripening. It was less effective when applied at full strength or to grains that had been freshly harvested. The same stimulatory effect was observed in par-fly after-ripened caryopses of nine different wild oat biotypes obtained from three different cropping regions of the world. When freshly harvested caryopses were re-tested with the commercial solution (100%) for just 7 days prior to placement on to distilled water, a much higher germination percentage was possible than seen with continuous smoke-water incubation. The stimulatory ability of smoke water was more closely matched to that of gibberellic acid than to potassium nitrate, which had little or no effect on freshly harvested caryopses. The smoke-water solution (5-100%) was tested on the germination of 18 other cool temperate arable weed species. All monocotyledonous species tested (viz. Avena sterilis ssp. ludoviciana L., Alopecurus myosuroides, Sorghum halepense, Phalaris paradoxa) responded positively, while those of the dicotyledonous species were either strongly stimulated (greater than or equal to 40% stimulation Malva neglecta), moderately stimulated (greater than or equal to 20% stimulation Galium aparine, Veronica persica), slightly stimulated (Polygonum persicaria, P pennsylvanicum, Fallopia convolvulus), unaffected (P. aviculare, Sinapis arvensis, Heracleum sphondylium, Angelica sylvestris, Mercurialis annua, Veronica hederifolia) or inhibited (Lamium purpureum). The optimal concentrations required to stimulate germination of the monocotyledonous species were similar to those observed for A. fatua (5-10%). However, for the dicotyledonous species slightly stronger solutions were required (10-20%). When the unaffected species were retested using a 10-day pre-chilling treatment, smoke water showed a small promotive response in three (S. arvensis, P. aviculare and V hederifolia) of the six species. When four different smoke-water solutions (Seed Starter (R), Regen 2000 (R), charred-wood solution and wheat-straw solution) were tested on two representative species (A. fatua and M. neglecta), three formulations were effective in promoting the germination of both species, while the fourth (charred-wood solution) was only active on A. fatua. The active concentrations were different for the four solutions. Three solutions were active in the 2-20% dilution range, while the fourth (Regen 2000 (R)) was only active in the 1-2% dilution range and was inhibitory at higher concentrations. These observations are discussed in the context that smoke may play an important ecological role in the management and control of introduced weeds in native and arable communities.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths. (C) 2001 Elsevier Science B.V. All rights reserved.

Subtropical drosophilids in Australia can be characterized by adult distribution across vegetation type and by height above forest floor

Understanding the pattern in which adult drosophilids of different species are distributed across and within different vegetation types is necessary for accurate interpretation of their local ecology and diversity. Such studies have been conducted mainly in temperate regions, and there is no basis for extrapolating their conclusions to tropical areas. This study describes the vertical distribution (0-20 m) of drosophilids attracted to banana baits in five different vegetation types in subtropical eastern Australia including open woodland, and rain-forest types. The distribution of most of the 15 common species could be characterized three-dimensionally by vegetation type and height above forest floor. Only one species, Scaptodrosophila lativittata, was common in all vegetation types and it was a canopy species in rain forests and a ground-level species in open woodland. Vertical distribution of some species clearly matched that of their larval hosts, but it did not in others. For example, the fungivore Leucophenga scutellata was mostly trapped well above the forest floor, yet it breeds at ground level, suggesting behavioural mode can influence vertical distributions. We conclude that the vertical dimension, although still poorly understood in relation to drosophilid habitats, needs to be taken into account when conducting and interpreting studies aimed at understanding drosophilid populations and communities in the subtropics.

The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

Scavenging of siliceous grain-boundary phase of 8-mol%-ytterbia-stabilized zirconia without additive

The grain-boundary conductivity (sigma (gb),) of 8-mol%-ytterbiastabilized zirconia increased markedly with heat treatment between 1000 degrees and 1300 degreesC with a slow heating rate (0.1 degreesC/min) before sintering. The extent of the sigma (gb) improvement was the same or larger than that via Al2O3 addition. The heat treatment did not affect the grain-interior conduction when sintered at 1600 degreesC, while Al2O3-derived scavenging significantly did, given the larger increment of total conductivity in the heat-treated sample. The formation of a silicon-containing phase in a discrete form was suggested as a possible route of scavenging the resistive phase from the correlation between average grain size and sigma (gb).

A classification of subantarctic Heard Island vegetation

The vascular and bryophyte floras of subantarctic Heard Island were classified using cluster analysis into six vegetation communities: Open Cushion Carpet, Mossy Feldmark, Wet Mixed Herbfield, Coastal Biotic Vegetation, Saltspray Vegetation, and Closed Cushion Carpet. Multidimensional scaling indicated that the vegetation communities were not well delineated but were continua. Discriminant analysis and a classification tree identified altitude, wind, peat depth, bryophyte cover and extent of bare ground, and particle size as discriminating variables. The combination of small area, glaciation, and harsh climate has resulted in reduced vegetation variety in comparison to those subantarctic islands north of the Antarctic Polar Front Zone. Some of the functional groups and vegetation communities found on warmer subantarctic islands are not present on Heard Island, notably ferns and sedges and fernbrakes and extensive mires, respectively.

N-15 natural abundance of fossil peat reflects the influence of animal-derived nitrogen on vegetation

delta(15)N signatures of fossil peat were used to interpret past ecosystem processes on tectonically active subantarctic Macquarie Island. By comparing past vegetation reconstructed from the fossil record with present-day vegetation analogues, our evidence strongly suggests that changes in the delta(15)N signatures of fossil peat at this location reflect mainly past changes in the proportion of plant nitrogen derived from animal sources. Associated with uplift above sea level over the past 8,500 years, fossil records in two peat deposits on the island chronicle a change from coastal vegetation with fur and elephant seal disturbance to the existing inland herbfield. Coupled with this change are synchronous changes in the delta(15)N signatures of peat layers. At two sites N-15-enriched peat delta(15)N signatures of up to +17parts per thousand were associated with a high abundance of pollen of the nitrophile Callitriche antarctica (Callitrichaceae). At one site fossil seal hair was also associated with enriched peat delta(15)N. Less N-15 enriched delta(15)N signatures (e.g. -1.9parts per thousand to +3.9parts per thousand) were measured in peat layers which lacked animal associated C. antarctica and Acaena spp. Interpretation of a third peat profile indicates continual occupation of a ridge site by burrowing petrels for most of the Holocene. We suggest that N-15 signatures of fossil peat remained relatively stable with time once deposited, providing a significant new tool for interpreting the palaeoecology.

Impact of point source pollution on nitrogen isotope signatures (delta N-15) of vegetation in SE Brazil

This study presents novel evidence that N-15 natural abundance can be used as a robust indicator to detect pollutant nitrogen in natural plant communities. Vegetation from the heavily polluted industrial area of Cubatao in Sao Paulo State, SE Brazil, was strongly N-15 depleted compared to plants at remote sites. Historic herbarium samples from Cubatao were significantly less N-15 depleted than extant plants, indicating that N-15 depletion of vegetation is associated with present-day nitrogen pollution in Cubatao. The heavy load of nitrogenous atmospheric pollutants in Cubatao provides a nitrogen source for plants, and strongly N-15 depleted air NH3 is likely to contribute to plant and soil N-15 depletion. Epiphytic plants from Cubatao were extremely N-15 depleted (average -10.9parts per thousand) contrasting with epiphytes at remote sites (averages -1.0parts per thousand and -3.0parts per thousand). Nitrogen isotope composition of vegetation provides a tool to determine input of pollutant nitrogen into plant communities. The strong isotopic change of epiphytes suggests that epiphytes are particularly sensitive biomonitors for atmospheric pollutant nitrogen.

Precursor scavenging of resistive grain-boundary phase in 8 mol % ytterbia-stabilized zirconia

The grain-boundary conduction of 8 mol % ytterbia-stabilized zirconia (8YbSZ) was improved markedly by precursor scavenging via the two-stage sintering process. The most significant increase in the grain-boundary conductivity was found when the sample, whose conductivity was higher than that via Al2O3-derived scavenging, was heat-treated at 1250degreesC for greater than or equal to 20 h. The formation of a stable Si-containing phase such as ZrSiO4 during the first-stage heat-treatment was suggested as one probable scavenging route from the optimal heat-treatment temperature (HTT), long duration time (>20 h) at HTT, and the stability of the formed phase up to sintering temperatures (1500degrees C). (C) 2002 The Electrochemical Society.