The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodynamics. For instance, for current J and magnetic field BS(J), we show that Maxwell's equations naturally hold. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. This article describes several properties of BS: we show it is self-adjoint, bounded, and extends to a compact operator on a Hilbert space. For vector fields that act like currents, we prove the curl operator is a left inverse to BS; thus the Biot-Savart operator is important in the study of curl eigenvalues, with applications to energy-minimization problems in geometry and physics. We conclude with two examples, which indicate our bounds are typically within an order of magnitude of being sharp.Comment: 24 pages (was 28 pages) Revised to include a new introduction, a detailed example, and results about helicity; other changes for readabilit

A novel TP53 splicing mutation in a Li-Fraumeni syndrome family: a patient with Wilms' tumour is not a mutation carrier.

We report a Li-Fraumeni syndrome family in which we have detected a splice acceptor mutation in intron 3 of TP53. The mutation affects one of the invariant residues at the splice acceptor site, as a result of which two aberrant transcripts are produced. A child with Wilms' tumour aged 3 years in this family was shown not to be a mutation carrier

Unsteady turbulence in tidal bores: Effects of bed roughness

A tidal bore is a wave propagating upstream as the tidal flow turns to rising. It forms during spring tide conditions when the flood tide is confined to a narrow funneled channel. To date, theoretical and numerical studies rely upon physical experiments to validate the developments, but the experimental data are limited mostly to visual observations and sometimes free-surface measurements. Herein turbulent velocity measurements were obtained in a large-size laboratory facility with a fine spatial and temporal resolution. The instantaneous velocity measurements showed rapid flow deceleration at all vertical elevations, and large fluctuations of all velocity components were recorded beneath the bore and secondary waves. A comparison between undular (nonbreaking) and breaking bores suggested some basic differences. In an undular bore, large velocity fluctuations were recorded beneath the first wave crest and the secondary waves showing a long-lasting effect after the bore passage. In a breaking bore, some large turbulent stresses were observed next to the shear zone in a region of high velocity gradients, while some transient flow recirculation was recorded next to the bed. The effects of bed roughness were tested further. The boundary friction contributed to some wave attenuation and dispersion, and the free-surface data showed some agreement with the wave dispersion theory for intermediate gravity waves. The instantaneous velocity data showed however a significant effect of the boundary roughness on the velocity field next to the boundary (z/d(o)< 0.2) for both undular and breaking bores. Overall the findings were consistent with field observations of tidal bores and highlighted the significant impact of undular (nonbreaking) bores on natural systems

Governors and directors: Competing models of corporate governance

Why do we use the term ‘corporate governance’ rather than ‘corporate direction’? Early British joint stock companies were normally managed by a single ‘governor’. The ‘court of governors’ or ‘board of directors’ emerged slowly as the ruling body for companies. By the nineteenth century, however, companies were typically run by directors while not-for-profit entities such as hospitals, schools and charitable bodies had governors. The nineteenth century saw steady refinement of the roles of company directors, often in response to corporate scandals, with a gradual change from the notion of the director as a ‘representative shareholder’ to the directors being seen collectively as ‘representatives of the shareholders’. Governors in not-for-profit entities, however, were regarded as having broader responsibilities. The term ‘governance’ itself suggests that corporate boards should be studied as ‘political’ entities rather than merely through economic lenses such as agency theory

Assessing the design of accounting modules across UK higher educational institutions

The purpose of this article is to uncover how accounting modules are designed across UK Higher Educational Institutions (HEIs). We carried out a content analysis of Undergraduate Year 1 Accounting Module Handbooks for a sample of 12 UK Universities. The study finds considerable heterogeneity concerning the way accounting modules are designed and delivered across the UK HE sector. Our findings reveal significant variations across the sector in terms of credit hours, module learning outcomes and assessment strategies. This research contributes to accounting/business education literature as no study has previously utilised a content analysis approach to understand how accounting modules are designed and delivered across UK HEIs

Cubic and hexagonal InGaAsN dilute arsenides by unintentional homogeneous incorporation of As into InGaN

Arsenic alloying is observed for epitaxial layers nominally intended to be In0.75Ga0.25N. Voids form beneath their interfaces with GaAs substrates, acting as sources of Ga + As out-diffusion into the growing epilayers. As a result, heteroepitaxial single-phase quaternary InxGa1-xAsyN1-y, films are formed with x similar to 0.55 and 0.05 menor que y menor que 0,10. While an undoped epilayer retains the wurtzite structure, a Mn-doped sample showed randomly spaced dopant segregations, which, together with a slightly higher As concentration, led to a transformation from the hexagonal to the twinned cubic phase

Physical Modelling of the Flow Field in an Undular Tidal Bore

A tidal bore may form in a converging channel with a funnel shape when the tidal range exceeds 6-9 m. The advancing surge has a major impact on the estuarine ecosystem. Physical modelling of an undular bore has been conducted based upon a quasi-steady flow analogy. The experimental data highlight rapid flow redistributions between successive wave troughs and crests as well as large bottom shear stress variations. The results suggest a sediment transport process combining scour beneath wave troughs associated with upward matter dispersion between a trough and the following wave crest. The process is repeated at each trough and significant sediment transport takes place with deposition in upstream intertidal zones. The conceptual model is supported by field observations showing murky waters after the bore passage and long-lasting chaotic waves

Turbulence measurements in positive surges and bores

A positive surge results from a sudden change in flow that increases the flow depth. New experiments were conducted in a large channel. Most positive surge tests were conducted with a horizontal bed slope, a constant flow rate and uncontrolled flow conditions. The only dependant variable was the downstream gate opening after closure. Detailed turbulence measurements were performed with high-temporal resolution using side-looking acoustic Doppler velocimetry. Two types of positive surge were observed: undular surge for Froude numbers less than 1.7, and weak (breaking) surges above. Instantaneous velocity measurements beneath advancing surges showed a marked effect of the surge passage on the velocity field. Streamwise velocities showed rapid flow deceleration at all vertical elevations. Large fluctuations of longitudinal and transverse velocities were recorded beneath the surges, including some unsteady flow recirculation beneath a weak surge front. Turbulent stresses were deduced from high-pass filtered data. The results showed large normal and tangential Reynolds stresses beneath the surges. A comparison between undular and weak surges suggested some major difference. In weak surge flows, the data showed rapid flow separation beneath the surge front. In undular surges, maximum Reynolds stresses were observed beneath and just before each wave crest behind the leading wave

Jasmonic acid-dependent regulation of seed dormancy following maternal herbivory in Arabidopsis

Maternal experience of abiotic environmental factors such as temperature and light are well known to control seed dormancy in many plant species. Maternal biotic stress alters offspring defence phenotypes, but whether it also affects seed dormancy remains unexplored. We exposed Arabidopsis thaliana plants to herbivory and investigated plasticity in germination and defence phenotypes in their offspring, along with the roles of phytohormone signalling in regulating maternal effects. Maternal herbivory resulted in the accumulation of jasmonic acid-isoleucine and loss of dormancy in seeds of stressed plants. Dormancy was also reduced by engineering seed-specific accumulation of jasmonic acid in transgenic plants. Loss of dormancy was dependent on an intact jasmonate signalling pathway and was associated with increased gibberellin content and reduced abscisic acid sensitivity during germination. Altered dormancy was only observed in the first generation following herbivory, whereas defence priming was maintained for at least two generations. Herbivory generates a jasmonic acid-dependent reduction in seed dormancy, mediated by alteration of gibberellin and abscisic acid signalling. This is a direct maternal effect, operating independently from transgenerational herbivore resistance priming

Bio-energy retains its mitigation potential under elevated CO2

Background If biofuels are to be a viable substitute for fossil fuels, it is essential that they retain their potential to mitigate climate change under future atmospheric conditions. Elevated atmospheric CO2 concentration [CO2] stimulates plant biomass production; however, the beneficial effects of increased production may be offset by higher energy costs in crop management. Methodology/Main findings We maintained full size poplar short rotation coppice (SRC) systems under both current ambient and future elevated [CO2] (550 ppm) and estimated their net energy and greenhouse gas balance. We show that a poplar SRC system is energy efficient and produces more energy than required for coppice management. Even more, elevated [CO2] will increase the net energy production and greenhouse gas balance of a SRC system with 18%. Managing the trees in shorter rotation cycles (i.e. 2 year cycles instead of 3 year cycles) will further enhance the benefits from elevated [CO2] on both the net energy and greenhouse gas balance. Conclusions/significance Adapting coppice management to the future atmospheric [CO2] is necessary to fully benefit from the climate mitigation potential of bio-energy systems. Further, a future increase in potential biomass production due to elevated [CO2] outweighs the increased production costs resulting in a northward extension of the area where SRC is greenhouse gas neutral. Currently, the main part of the European terrestrial carbon sink is found in forest biomass and attributed to harvesting less than the annual growth in wood. Because SRC is intensively managed, with a higher turnover in wood production than conventional forest, northward expansion of SRC is likely to erode the European terrestrial carbon sink