501 research outputs found

    Geometric characterization of nodal domains: the area-to-perimeter ratio

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    In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio ρ\rho between the area of a domain and its perimeter, measured in units of the wavelength 1/E1/\sqrt{E}. We show that the distribution function P(ρ)P(\rho) can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution, and show that it is supported by an interval, which is independent of the properties of the surface. In systems which are chaotic, or in random-waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wave functions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to, and provides a new point of view on isoperimetric inequalities.Comment: 22 pages, 11 figure

    Theory for phonon-induced superconductivity in MgB2_2

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    We analyze superonductivity in MgB2_2 observed below Tc=39T_c=39 K resulting from electron-phonon coupling involving a mode at ω1=24\hbar \omega_1 = 24 meV and most importantly the in-plane B-B E2gE_{2g} vibration at ω2=67\hbar \omega_2=67 meV. The quasiparticles originating from π\pi- and σ\sigma-states couple strongly to the low-frequency mode and the E2gE_{2g}-vibrations respectively. Using two-band Eliashberg theory, λπ=1.4\lambda_{\pi} = 1.4 and λσ=0.7\lambda_{\sigma} = 0.7, we calculate the gap functions Δi(ω,0)\Delta^{i}(\omega,0) (i=πi=\pi, σ\sigma). Our results provide an explanation of recent tunneling experiments. We get Hc2ab/Hc2c3.9H^{ab}_{c_2}/H^{c}_{c_2} \approx 3.9.Comment: revised version, accepted for publication in PR

    Reculturing schools in England: how ‘cult’ values in education policy discourse influence the construction of practitioner identities and work orientations

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    The imperative of continuous improvement has now become normative in education policy discourse, typically framed as setting ‘aspirational’ targets for pupil performance as a prerequisite for gaining competitive advantage in the global economy. In this context, teachers, leaders, teacher assistants and other practitioners working in schools across England have been under increasing pressure to raise standards. This article focuses on how values are deployed in reculturing and regulating practitioners to develop identities and work orientations which are congruent with the policymakers’ agendas. G.H. Mead’s concept of ‘cult’ values illuminates the process of fostering homogeneity with the dominant policy discourse through an inclusion/exclusion dynamic. Interview data collected in two primary schools revealed a significant convergence of practitioner discourse with policy objectives. Delivering improvement affects how practitioners talk about their work and see themselves as educators. The ‘cult’ of continuous improvement appears to inhibit a critical approach to the implementation of education policies by school practitioners in their everyday work

    Polygenic risk scores for Alzheimer's disease are related to dementia risk in APOE ɛ4 negatives

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    Introduction: Studies examining the effect of polygenic risk scores (PRS) for Alzheimer's disease (AD) and apolipoprotein E (APOE) genotype on incident dementia in very old individuals are lacking. / Methods: A population‐based sample of 2052 individuals ages 70 to 111, from Sweden, was followed in relation to dementia. AD‐PRSs including 39, 57, 1333, and 13,942 single nucleotide polymorphisms (SNPs) were used. / Results: AD‐PRSs (including 39 or 57 SNPs) were associated with dementia (57‐SNPs AD‐PRS: hazard ratio 1.09, confidence interval 1.01–1.19, P = .03), particularly in APOE ɛ4 non‐carriers (57‐SNPs AD‐PRS: 1.15, 1.05–1.27, P = 4 × 10–3, 39‐SNPs AD‐PRS: 1.22, 1.10–1.35, P = 2 × 10–4). No association was found with the other AD‐PRSs. Further, APOE ɛ4 was associated with increased risk of dementia (1.60, 1.35–1.92, P = 1 × 10–7). In those aged ≥95 years, the results were similar for the AD‐PRSs, while APOE ɛ4 only predicted dementia in the low‐risk tertile of AD‐PRSs. / Discussion: These results provide information to identify individuals at increased risk of dementia

    Fish consumption patterns and hair mercury levels in children and their mothers in 17 EU countries

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    The toxicity of methylmercury (MeHg) in humans is well established and the main source of exposure is via the consumption of large marine fish and mammals. Of particular concern are the potential neurodevelopmental effects of early life exposure to low-levels of MeHg. Therefore, it is important that pregnant women, children and women of childbearing age are, as far as possible, protected from MeHg exposure.Within the European project DEMOCOPHES, we have analyzed mercury (Hg) in hair in 1799 mother–child pairs from 17 European countries using a strictly harmonized protocol for mercury analysis. Parallel, harmonized questionnaires on dietary habits provided information on consumption patterns of fish and marine products. After hierarchical cluster analysis of consumption habits of the mother–child pairs, the DEMOCOPHES cohort can be classified into two branches of approximately similar size: one with high fish consumption (H) and another with low consumption (L). All countries have representatives in both branches, but Belgium, Denmark, Spain, Portugal and Sweden have twice as many or more mother–child pairs in H than in L. For Switzerland, Czech Republic, Hungary, Poland, Romania, Slovenia and Slovakia the situation is the opposite, with more representatives in L than H.There is a strong correlation (r=0.72) in hair mercury concentration between the mother and child in the same family, which indicates that they have a similar exposure situation. The clustering of mother–child pairs on basis of their fish consumption revealed some interesting patterns. One is that for the same sea fish consumption, other food items of marine origin, like seafood products or shellfish, contribute significantly to the mercury levels in hair. We conclude that additional studies are needed to assess and quantify exposure to mercury from seafood products, in particular. The cluster analysis also showed that 95% of mothers who consume once per week fish only, and no other marine products, have mercury levels 0.55 µg/g. Thus, the 95th percentile of the distribution in this group is only around half the US-EPA recommended threshold of 1 µg/g mercury in hair. Consumption of freshwater fish played a minor role in contributing to mercury exposure in the studied cohort.The DEMOCOPHES data shows that there are significant differences in MeHg exposure across the EU and that exposure is highly correlated with consumption of fish and marine products. Fish and marine products are key components of a healthy human diet and are important both traditionally and culturally in many parts of Europe. Therefore, the communication of the potential risks of mercury exposure needs to be carefully balanced to take into account traditional and cultural values as well as the potential health benefits from fish consumption. European harmonized human biomonitoring programs provide an additional dimension to national HMB programs and can assist national authorities to tailor mitigation and adaptation strategies (dietary advice, risk communication, etc.) to their country’s specific requirements
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