On the group-velocity property for wave-activity conservation laws

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Sodomy laws and gender variance in Tahiti and Hawai‘i

In both Hawaiian and Tahitian, the central meaning of mahu denotes gender-variant individuals, particularly male-bodied persons who have a significant investment in femininity. However, in Hawai‘i, unlike Tahiti, the word mahu is now more commonly used as an insult against gay or transgender people. The negative connotation of the term in Hawaiian indexes lower levels of social acceptability for mahu identity on O‘ahu (Hawai‘i’s most populous island) as compared to Tahiti. The article argues that these differences are partly due to a historical legacy of sexually repressive laws. The article traces the history of sodomy laws in these two Polynesian societies and argues that this history supports the hypothesis that sodomy laws (in conjunction with such social processes as urbanisation and Christianisation) are partially to blame for the diminished social status of mahu on O‘ahu. A different social and legal history in Tahiti accounts for the fact that the loss of social status experienced by Tahitian mahu has been lesser than that of their Hawaiian counterparts.

Deficits in orthographic knowledge in children poor at rapid automatized naming (RAN) tasks?

The degree to which orthographic knowledge accounts for the link between Rapid Automatized Naming (RAN) and reading is contested, with mixed results reported. This longitudinal study compared two groups of 10-11 year old children, a low RAN group (N=69) and matched controls (N=74) on various measures of orthographic knowledge. The low RAN group showed a deficit in orthographic knowledge, both at the level of sub-word letter sequences and of whole words, as well as an unexpected strength in orthographic learning. Our findings underline the persistence of RAN-related reading problems, and raise questions about reading strategies in this group.

Educational attainment in poor comprehenders

To date, only one study has investigated educational attainment in poor (reading) comprehenders, providing evidence of poor performance on national UK school tests at age 11 years relative to peers (Cain & Oakhill, 2006). In the present study, we adopted a longitudinal approach, tracking attainment on such tests from 11 years to the end of compulsory schooling in the UK (age 16 years). We aimed to investigate the proposal that educational weaknesses (defined as poor performance on national assessments) might become more pronounced over time, as the curriculum places increasing demands on reading comprehension. Participants comprised 15 poor comprehenders and 15 controls; groups were matched for chronological age, nonverbal reasoning ability and decoding skill. Children were identified at age 9 years using standardised measures of nonverbal reasoning, decoding and reading comprehension. These measures, along with a measure of oral vocabulary knowledge, were repeated at age 11 years. Data on educational attainment were collected from all participants (N = 30) at age 11 and from a subgroup (n = 21) at 16 years. Compared to controls, educational attainment in poor comprehenders was lower at ages 11 and 16 years, an effect that was significant at 11 years. When poor comprehenders were compared to national performance levels, they showed significantly lower performance at both time points. Low educational attainment was not evident for all poor comprehenders. Nonetheless, our findings point to a link between reading comprehension difficulties in mid to late childhood and poor educational outcomes at ages 11 and 16 years. At these ages, pupils in the UK are making key transitions: they move from primary to secondary schools at 11, and out of compulsory schooling at 16.

Financial services for the poor within the formal/informal nexus in sub-Saharan Africa

This paper draws upon fieldwork undertaken across Kenya, Zambia, Mozambique and South Africa to present a reflective overview of the use of financial services amongst the poorest members of society. It considers the role that access to a portfolio of financial products and services may have as a contributory factor in poverty alleviation, but also how inappropriate use of these mechanisms may exacerbate a descent into poverty. This work draws upon the notions of poverty pools and the rise of fall of low income households in and out of poverty, alongside the contributory nature of vicious cycles of economic and political poverty. Drawing on fieldwork experiences it presents a synopsis of the types of financial mechanisms commonly in use on the African continent, as well as examples of public, private and civil society partnerships that are producing services specifically tailored for those in extreme and absolute poverty.

Workers with elderly dependants: employment law’s response to the latest care-giving conundrum

This paper considers how employment laws are being used in response to what we have termed ‘the eldercare/workplace conundrum’. It is well known that people are now living longer but health is still failing in a significant percentage of older people, meaning that many adults require care for longer, albeit to varying degrees and for varying amounts of time. Many of these individuals will receive care from relatives or close friends who are participating in the labour market: this is increasingly likely as adults are expected / wanting to remain in paid work for longer, often into their 60s and 70s. The requirements of elderly dependants can cause these workers huge difficulties and dilemmas as they attempt, across time, to accommodate the particular needs of the person for whom they wish to provide care, often a loved one, and meet the particular demands of their employment relationship. In this paper we consider why this is an area of social policy that warrants effective legal engagement and consider, drawing on various examples of legal responses in other countries that face similar conundrums, what might improve legal engagement in this area.

Recovery based on plot experiments is a poor predictor of landscape-level population impacts of agricultural pesticides

Current European Union regulatory risk assessment allows application of pesticides provided that recovery of nontarget arthropods in-crop occurs within a year. Despite the long-established theory of source-sink dynamics, risk assessment ignores depletion of surrounding populations and typical field trials are restricted to plot-scale experiments. In the present study, the authors used agent-based modeling of 2 contrasting invertebrates, a spider and a beetle, to assess how the area of pesticide application and environmental half-life affect the assessment of recovery at the plot scale and impact the population at the landscape scale. Small-scale plot experiments were simulated for pesticides with different application rates and environmental half-lives. The same pesticides were then evaluated at the landscape scale (10 km × 10 km) assuming continuous year-on-year usage. The authors' results show that recovery time estimated from plot experiments is a poor indicator of long-term population impact at the landscape level and that the spatial scale of pesticide application strongly determines population-level impact. This raises serious doubts as to the utility of plot-recovery experiments in pesticide regulatory risk assessment for population-level protection. Predictions from the model are supported by empirical evidence from a series of studies carried out in the decade starting in 1988. The issues raised then can now be addressed using simulation. Prediction of impacts at landscape scales should be more widely used in assessing the risks posed by environmental stressors.

Poor survival on an artificial diet of two genotypes of the aphid Myzus persicae: a fitness cost of insecticide resistance?

A fully susceptible genotype (4106A) of Myzus persicae survived the longest on an artificial diet and, in several of the eight replicates, monitoring was terminated when the culture was still thriving. A genotype with elevated carboxylesterase FE4 at the R3 level (800F) had a mean survival of only 98.13 days, whereas 794J, which combines R3 E4 carboxylesterase with target-site resistance (knockdown resistance), survived for the even shorter mean time of 84.38 days. The poorer survival of the two genotypes with extremely elevated carboxylesterase-resistance was not the result of a reluctance to transfer to new diet at each diet change. Although available for only two replicates, a revertant clone of 794J (794Jrev), which has the same genotype as 794J but the amplified E4 genes are not expressed leading to a fully susceptible phenotype, did not appear to survive any better than this clone. This suggests that the poor survival on an artificial diet of the extreme-carboxylesterase genotypes is not the result of the cost of over-producing the enzyme. The frequency of insecticide-resistant genotypes is low in the population until insecticide is applied, indicating that they have reduced fitness, although this does not necessarily reflect a direct cost of expressing the resistance mechanism.

Dating the Thera (Santorin) eruption: evidence versus poor scholarship, and the end of the low chronology

The date of the Late Bronze Age Minoan eruption of the Thera volcano has provoked much debate among archaeologists, not least in a recent issue of Antiquity (‘Bronze Age catastrophe and modern controversy: dating the Santorini eruption’, March 2014). Here, the authors respond to those recent contributions, citing evidence that closes the gap between the conclusions offered by previous typological, stratigraphic and radiometric dating techniques. They reject the need to choose between alternative approaches to the problem and make a case for the synchronisation of eastern Mediterranean and Egyptian chronologies with agreement on a ‘high’ date in the late seventeenth century BC for the Thera eruption.

Carotenoids but not flavonoids are associated with improvements in spatial working memory in younger adults in a flavonoid-rich v. -poor fruit and vegetable intervention study

Findings from animal studies suggest that components of fruit and vegetables (F&V) may protect against, and even reverse, age-related decline(1,2) in aspects of cognitive functioning such as spatial working memory (SWM). Human subjects in vivo and in vitro studies indicate that anti-inflammatory, anti-oxidant and cell-signalling properties of flavonoids and carotenoids, non-nutrient components of F&V, may underpin this protective effect(3–5). The Flavonoid University of Reading Study (FLAVURS), designed to explore the dose-response relationship between dietary F&V flavonoids and CVD, enabled the investigation of such an association with SWM. FLAVURS is an 18-week parallel three-arm randomised controlled dietary intervention trial with four time points, measured at 6-weekly intervals from baseline. Low F&V consumers at risk of CVD aged 26–70 years were randomly assigned to high flavonoid (HF), low flavonoid (LF) or control group. F&V intake increased by two daily 80 g portions every 6 weeks, with either HF or LF F&V, in addition to each participant's habitual diet, while controls maintained their habitual diet. At each visit, participants completed a cognitive test battery with SWM as the primary outcome. The HF group showed significantly higher levels of urinary flavonoids than LF or controls at 12 weeks (P<0.001) as expected, but surprisingly only higher levels than LF at 18 weeks (P<0.01). The LF group showed higher levels of plasma carotenoids than the other groups at 18 weeks (P<0.001). No group differences were found for SWM overall, however, age-group sub-analyses (26–50 and 51–70 years of age) showed differences from 0 to 18 weeks for younger adults, with LF improving significantly more than the other two groups on SWM (P<0.05). As nutritional absorption is known to decrease with age, separate stepwise regressions were performed on the two age groups irrespective of dietary group, with urinary flavonoids and plasma carotenoids as predictors. For younger adults, improved SWM performance from 0 to 18 weeks was associated with higher carotenoid levels, β=0.28, t(55)=2.10, P<0.05, accounting for 7.5% of the variance, R2=0.075, F(1,54)=4.41, P=0.040. For older adults, no between-group SWM differences were found. Findings suggest that F&V-based flavonoids and carotenoids may provide benefits for cognitive function, and that carotenoids in particular may improve cognitive performance in SWM. Given that these benefits were restricted to younger adults, future work is needed to test the reliability of this finding, as well as determine the mechanisms by which age-dependent differences in F&V responsiveness occur.

A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.