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.

"Racism in a Melting Pot...?" Trinidadian mid-life transnational migrants' views on race and colour-class on return to their homes of descent

This paper deals with second-generation, one-and-a-half generation and ‘‘prolonged sojourner” Trinidadian transnational migrants, who have decided to ‘return’ to the birthplace of their parents. Based on 40 in-depth interviews, the paper considers both the positive and critical things that these youthful transnational migrants report about returning to, and living in, this multi-ethnic plural society and the salience of racial and colour-class stratification as part of their return migration experiences. Our qualitative analysis is based on the narratives provided by these youthful returnees, as relayed ‘‘in their own words”, presenting critical reflections on racism, racial identities and experiences as transnational Trinidadians. It is clear that it is contexts such as contemporary working environments, family and community that act as the reference points for the adaptation ‘‘back home” of this strongly middle-class cohort. We accordingly encounter a diverse, sometimes contesting set of racial issues that emerge as salient concerns for these returnees. The consensus is that matters racial remain as formidable legacies in the hierarchical stratification of Trinidadian society for a sizeable number. Many of our respondents reported the positive aspects of racial affirmation on return. But for another sub-set, the fact that multi-ethnic and multi-cultural mixing are proudly embraced in Trinidad meant that it was felt that return experiences were not overly hindered, or blighted by obstacles of race and colour-class. For these returnees, Trinidad and Tobago is seen as representing a 21st century ‘‘Melting Pot”. But for others the continued existence of racial divisions within society – between ethnic groups and among those of different skin shades – was lamented. In the views of these respondents, too much racial power is still ascribed to ‘near-whiteness’. But for the most part, the returnees felt that where race played a part in their new lives, this generally served to advantage them. However, although the situation in Trinidad appears to have been moderated by assumptions that it remains a racial ‘Melting Pot’, the analysis strongly suggests that the colour-class system of stratification is still playing an essential role, along with racial stereotyping in society at large.

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.

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.