Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Record of natural and anthropogenic changes in reef environments (Barbados West Indies) using laser ablation ICP-MS and sclerochronology on coral cores

Coral growth rate can be affected by environmental parameters such as seawater temperature, depth, and light intensity. The natural reef environment is also disturbed by human influences such as anthropogenic pollutants, which in Barbados are released close to the reefs. Here we describe a relatively new method of assessing the history of pollution and explain how these effects have influenced the coral communities off the west coast of Barbados. We evaluate the relative impact of both anthropogenic pollutants and natural stresses. Sclerochronology documents framework and skeletal growth rate and records pollution history (recorded as reduced growth) for a suite of sampled Montastraea annularis coral cores. X-radiography shows annual growth band patterns of the corals extending back over several decades and indicates significantly lower growth rate in polluted sites. Results using laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) on the whole sample (aragonite, organic matter, trapped particulate matter, etc.), have shown contrasting concentrations of the trace elements (Cu, Sn, Zn, and Pb) between corals at different locations and within a single coral. Deepwater corals 7 km apart, record different levels of Pb and Sn, suggesting that a current transported the metal pollution in the water. In addition, the 1995 hurricanes are associated with anomalous values for Sn and Cu from most sites. These are believed to result from dispersion of nearshore polluted water. We compared the concentrations of trace elements in the coral growth of particular years to those in the relevant contemporaneous seawater. Mean values for the concentration factor in the coral, relative to the water, ranged from 10 for Cu and Ni to 2.4 and 0.7 for Cd and Zn, respectively. Although the uncertainties are large (60-80%), the coral record enabled us to demonstrate the possibility of calculating a history of seawater pollution for these elements from the 1940s to 1997. Our values were much higher than those obtained from analysis of carefully cleaned coral aragonite; they demonstrate the incorporation of more contamination including that from particulate material as well as dissolved metals.

High-resolution, unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia

Accuracy and mesh generation are key issues for the high-resolution hydrodynamic modelling of the whole Great Barrier Reef. Our objective is to generate suitable unstructured grids that can resolve topological and dynamical features like tidal jets and recirculation eddies in the wake of islands. A new strategy is suggested to refine the mesh in areas of interest taking into account the bathymetric field and an approximated distance to islands and reefs. Such a distance is obtained by solving an elliptic differential operator, with specific boundary conditions. Meshes produced illustrate both the validity and the efficiency of the adaptive strategy. Selection of refinement and geometrical parameters is discussed. (c) 2006 Elsevier Ltd. All rights reserved.

Grassland leafhoppers (Hemiptera: Auchenorrhyncha) as indicators of habitat condition - a comparison of between-site and between-year differences in assemblage composition

The Auchenorrhyncha (leafhoppers) show great potential as indicators of grassland habitat quality, which would make them useful as a conservation tool. However, they are known to have labile populations. The relative importance of site identity and the year of sampling in the composition of leafhopper assemblages on chalk grassland are assessed for two sets of sites sampled twice. The study included a total of 95 sites (one set of 54, the other of 41), and demonstrated that for both sets the vegetation community and geographical location had high explanatory value, while the influence of year was small. The conclusion is that, notwithstanding population fluctuations, the leafhopper assemblages are a good indicator of habitat quality, and represent a potentially valuable tool in grassland conservation and restoration.

Computer modelling and estimation of recruitment patterns of non-branching coral colonies at three sites in Wakatobi Marine Park, S.E. Sulawesi, Indonesia; implications for coral reef conservation

We have studied growth and estimated recruitment of massive coral colonies at three sites, Kaledupa, Hoga and Sampela, separated by about 1.5 km in the Wakatobi Marine National Park, S.E. Sulawesi, Indonesia. There was significantly higher species richness (P<0.05), coral cover (P<0.05) and rugosity (P<0.01) at Kaledupa than at Sampela. A model for coral reef growth has been developed based on a rational polynomial function, where dx/dt is an index of coral growth with time; W is the variable (for example, coral weight, coral length or coral area), up to the power of n in the numerator and m in the denominator; a1……an and b1…bm are constants. The values for n and m represent the degree of the polynomial, and can relate to the morphology of the coral. The model was used to simulate typical coral growth curves, and tested using published data obtained by weighing coral colonies underwater in reefs on the south-west coast of Curaçao [‘Neth. J. Sea Res. 10 (1976) 285’]. The model proved an accurate fit to the data, and parameters were obtained for a number of coral species. Surface area data was obtained on over 1200 massive corals at three different sites in the Wakatobi Marine National Park, S.E. Sulawesi, Indonesia. The year of an individual's recruitment was calculated from knowledge of the growth rate modified by application of the rational polynomial model. The estimated pattern of recruitment was variable, with little numbers of massive corals settling and growing before 1950 at the heavily used site, Sampela, relative to the reef site with little or no human use, Kaledupa, and the intermediate site, Hoga. There was a significantly greater sedimentation rate at Sampela than at either Kaledupa (P<0.0001) or Hoga (P<0.0005). The relative mean abundance of fish families present at the reef crests at the three sites, determined using digital video photography, did not correlate with sedimentation rates, underwater visibility or lack of large non-branching coral colonies. Radial growth rates of three genera of non-branching corals were significantly lower at Sampela than at Kaledupa or at Hoga, and there was a high correlation (r=0.89) between radial growth rates and underwater visibility. Porites spp. was the most abundant coral over all the sites and at all depths followed by Favites (P<0.04) and Favia spp. (P<0.03). Colony ages of Porites corals were significantly lower at the 5 m reef flat on the Sampela reef than at the same depth on both other reefs (P<0.005). At Sampela, only 2.8% of corals on the 5 m reef crest are of a size to have survived from before 1950. The Scleractinian coral community of Sampela is severely impacted by depositing sediments which can lead to the suffocation of corals, whilst also decreasing light penetration resulting in decreased growth and calcification rates. The net loss of material from Sampela, if not checked, could result in the loss of this protective barrier which would be to the detriment of the sublittoral sand flats and hence the Sampela village.

The effect of learning condition on perceptual anticipation, awareness, and visual search

The efficacy of explicit and implicit learning paradigms was examined during the very early stages of learning the perceptual-motor anticipation task of predicting ball direction from temporally occluded footage of soccer penalty kicks. In addition, the effect of instructional condition on point-of-gaze during learning was examined. A significant improvement in horizontal prediction accuracy was observed in the explicit learning group; however, similar improvement was evident in a placebo group who watched footage of soccer matches. Only the explicit learning intervention resulted in changes in eye movement behaviour and increased awareness of relevant postural cues. Results are discussed in terms of methodological and practical issues regarding the employment of implicit perceptual training interventions. (c) 2005 Elsevier B.V. All rights reserved.

The effect of a perceptual cognitive task on exercise performance: the dual-task condition after brain injury

Objective: To examine the effect of additional cognitive demand on cycling performance in individuals with acquired brain injury (ABI). Design: Prospective observational study. Setting: Rivermead Rehabilitation Centre. Participants: Ten individuals with ABI ( 7 men, 3 women) ( traumatic brain injury 7, tumour 1, stroke 2) and 10 healthy controls ( 6 men, 4 women). Intervention: Individuals were asked to maintain a set cadence during a three-stage incremental cycling test in both single-task ( no additional task) and dual-task ( whilst performing an additional cognitive task) conditions. Results: The ABI group showed a slight slowing in cadence in stages 1 and 3 of the graded exercise test from the single-to the dual-task condition, although this was not significant ( p less than or equal to 0.05). The control group showed no slowing of cadence at any incremental stage. When directly comparing the ABI with the control group, the change in cadence observed in dual-task conditions was only significantly different in stage 3 ( p less than or equal to 0.05). Conclusions: Clinicians should be aware of the possibility that giving additional cognitive tasks ( such as monitoring exercise intensity) while individuals with acquired brain injury are performing exercises may detrimentally affect performance. The effect may be more marked when the individuals are performing exercise at higher intensities.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Fine root condition relates to visible crown damage in Norway spruce on acidified soils

Allochthonous Norway spruce stands in the Kysucké Beskydy Mts. (north-western Slovakia) have been exposed to substantial acid deposition in the recent past and grow in acidified soil conditions with mean pH of about 4.0 in the topsoil. We selected 90 spruce trees representing 30 triples of different crown status: healthy, stressed and declining to assess the relationship between crown and fine root status. Sequential coring and in-growth bags were applied to each triplet to investigate fine root biomass and growth in the soil depths of 0-10 and 10-20 cm. Fine root quantity (biomass and necromass), turnover (production over standing stock), morphological features (specific root length, root tip density) and chemical properties (Ca:Al molar ratio) were compared among the abovementioned health status categories. Living fine root biomass decreased with increasing stress, while the ratio of living to dead biomass increased. Annual fine root production decreased and specific root length increased in stressed trees when compared to healthy or declining trees, a situation which may be related to the position of trees in the canopy (healthy and declining – dominant, stressed – co-dominant). The Ca:Al ratio decreased with increasing crown damage, indicating a decreased ability to filter out aluminium. In conclusion, fine root status appears to be linked to visible crown damage and can be used as a tree health indicator.