Double-diffusive convection has been well studied in geophysical contexts, but detailed investigations of the regimes characteristic of stellar or planetary interiors have only recently become feasible. Since most astrophysical fluids are electrically conducting, it is possible that magnetic fields play a role in either enhancing or suppressing double-diffusive convection, but to date there have been no numerical investigations of such possibilities. Here we study the effects of a vertical background magnetic field (aligned with the gravitational axis) on the linear stability and nonlinear saturation of fingering (thermohaline) convection, through a combination of theoretical work and direct numerical simulations (DNSs). We find that a vertical magnetic field rigidifies the fingers along the vertical direction which has the remarkable effect of enhancing vertical mixing. We propose a simple analytical model for mixing by magnetized fingering convection, and argue that magnetic effects may help explain discrepancies between theoretical and observed mixing rates in low-mass red giant branch (RGB) stars. Other implications of our findings are also discussed.

The profiles of the broad emission lines of active galactic nuclei (AGNs) and the time delays in their response to changes in the ionizing continuum ("lags") give information about the structure and kinematics of the inner regions of AGNs. Line profiles are also our main way of estimating the masses of the supermassive black holes (SMBHs). However, the profiles often show ill-understood, asymmetric structure and velocity-dependent lags vary with time. Here we show that partial obscuration of the broad-line region (BLR) by outflowing, compact, dusty clumps produces asymmetries and velocity-dependent lags similar to those observed. Our model explains previously inexplicable changes in the ratios of the hydrogen lines with time and velocity, the lack of correlation of changes in line profiles with variability of the central engine, the velocity dependence of lags, and the change of lags with time. We propose that changes on timescales longer than the light-crossing time do not come from dynamical changes in the BLR, but are a natural result of the effect of outflowing dusty clumps driven by radiation pressure acting on the dust. The motion of these clumps offers an explanation of long-term changes in polarization. The effects of the dust complicate the study of the structure and kinematics of the BLR and the search for sub-parsec SMBH binaries. Partial obscuration of the accretion disc can also provide the local fluctuations in luminosity that can explain sizes deduced from microlensing.

Men's professional football is the biggest sport in the world, producing (by our estimate) US $33 billion a year. All is not well in the sector, however, with regular scandals raising questions about the role of money in the sport. The 2015 turmoil around FIFA is obviously the most well known example, creating a crisis in confidence in the sector. This study examines these questions, and the financial integrity weaknesses they reveal; it also offers ideas to strengthen the weaknesses. The study argues that football's financial integrity weaknesses extend far beyond FIFA. These weaknesses have emerged largely because the sector is dominated by a small elite of clubs, players and owners centered in Europe's top leagues. The thousands of clubs beyond this elite have very little resources, constituting a vast base of 'have-nots' in football's financial pyramid. This pyramid developed in recent decades, fuelled by concentrated growth in new revenue sources (like sponsorships, and broadcasting). The growth has also led to increasingly complex transactions-in player transfers, club ownership and financing (and more)-and an expansion in opportunities for illicit practices like match-fixing, money laundering and human trafficking. We argue that football's governing bodies-including FIFA-helped establish this pyramid. We explore the structural weaknesses of this pyramid by looking at five pillars of financial integrity (using data drawn from UEFA, FIFA, clubs, primary research, and interviews). In the first pillar of Financial Transparency and Literacy we find that a vast majority of the world's clubs and governing bodies publish no financial data, leaving a vast dark space with no transparency. In the second pillar of Financial Sustainability we estimate that a majority of global clubs and governing bodies are at 'medium to high risk' of financial failure. We find, additionally, that European tax debts have grown despite Financial Fair Play, and confederations and FIFA contribute to a pattern of weak Fiscal Responsibility. We then create a new metric of Financial Concentration and find that the football sector is at 'high risk' of over-concentration, which poses existential questions for many clubs and even leagues. In the final pillar of Social Responsibility and Moral Reputation, we find that football's governing bodies face a crisis of legitimacy stemming from a failure to tackle moral turpitude, set standards and regulate effectively. We suggest a set of reforms to restructure FIFA in particular, separating its functions and stressing its regulatory role.

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Summary In the course of gravel working at Poltalloch, Argyll,four Early Bronze Age graves were discovered. Grave 1 was largely destroyed but Graves 2–4 produced a beaker, two food vessels and a plano-convex knife, all of which were associated with inhumation burials. The excavations were carried out as part of a larger project, not described here, which revealed an extensive occupation area, with first millennium be and later levels.