We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with vertical and horizontal temperature gradients. In particular, the interaction of rotation with the horizontal temperature gradient drives a ‘thermal wind’ shear flow whose strength is controlled by the horizontal temperature gradient. Varying this parameter therefore systematically alters the ordering of the shearing time scale, the convective time scale and the correlation time scale. We demonstrate that quasilinear-type approximations work well when the shearing time scale or the correlation time scale is sufficiently short. In all cases, the generalised quasilinear approximation systematically outperforms the quasilinear approximation. We discuss the consequences for statistical theories of turbulence interacting with mean gradients.

This review considers current evidence on physical activity and dietary behaviours in the context of prostate cancer prevention and survivorship outcomes. Prostate cancer is the second most common cancer amongst men, with over 1⋅4 million newly diagnosed cases globally each year. Due to earlier detection via screening and advances in treatments, survival rates are amongst the highest of all cancer populations. However, hormone treatments (i.e. androgen deprivation therapy) can lead to undesirable body composition changes, increased fatigue and reduced health-related quality of life, which can impair the overall wellbeing of men living with and beyond prostate cancer. Existing research has only provided limited evidence that physical activity and nutrition can impact a man's risk of prostate cancer but cohort studies suggest they can influence survival outcomes after diagnosis. Additionally, data from observational and intervention studies suggest that habitual physical activity (or structured exercise) and healthy diets can help to ameliorate hormone-related treatment side-effects. Current physical activity guidelines state that prostate cancer patients should complete at least three sessions of moderate-intensity aerobic exercise per week, along with two resistance exercise sessions, but dietary guidelines for prostate cancer patients are less well defined. In conclusion, regular physical activity and nutritional interventions may improve survival outcomes and attenuate some adverse side-effects of hormone treatments in men with prostate cancer. However, further research is required to improve our understanding of the health impacts of physical activity (including structured exercise) and nutrition in relation to prostate cancer prevention and survivorship.

Platinum-group minerals (PGM) from placer deposits in Colombia, California, Oregon and Alaska were investigated with the electron microprobe, proton microprobe (μ-PIXE) and ion probe to analyse their major and trace element contents and 187Os/186Os isotopic ratios. Most of the grains in the samples investigated proved to be essentially homogeneous alloys of Pt-Fe and Os-Ir-Ru although a few of them contained inclusions of other PGM such as cooperite and laurite. Detailed analyses were undertaken on the Os-Ir-Ru alloy phases.

The 187Os/186Os isotope ratios fell into a range from 1.005 to 1.156 and are consistent with data published on PGM from other placer deposits from these regions. The ratios, together with the trace element data (and in particular the low rhenium content) determined by ion probe and μ-PIXE, indicate that crustal osmium was not incorporated in the grains and that no significant evolution of the 187Os/186Os ratios occurred during their history. These data, along with mineralogical and textural evidence, are consistent with a mantle origin for the grains through ultramafic intrusions, although the data do not entirely rule out alternative interpretations.

We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip and diffusion-dominated vapour transport are taken into account. A matched asymptotic analysis in the limit of small slip is used to derive a generalization of Tanner’s law that takes account of the effect of mass transfer. We find a criterion for when the contact-set radius close to extinction evolves as the square root of the time remaining until extinction – the famous $d^{2}$-law. However, for a sufficiently large rate of evaporation, our analysis predicts that a (slightly different) ‘$d^{13/7}$-law’ is more appropriate. Our asymptotic results are validated by comparison with numerical simulations.

We investigate the effect of mass transfer on the evolution of a thin, two-dimensional, partially wetting drop. While the effects of viscous dissipation, capillarity, slip and uniform mass transfer are taken into account, other effects, such as gravity, surface tension gradients, vapour transport and heat transport, are neglected in favour of mathematical tractability. Our focus is on a matched-asymptotic analysis in the small-slip limit, which reveals that the leading-order outer formulation and contact-line law depend delicately on both the sign and the size of the mass transfer flux. This leads, in particular, to novel generalisations of Tanner's law. We analyse the resulting evolution of the drop on the timescale of mass transfer and validate the leading-order predictions by comparison with preliminary numerical simulations. Finally, we outline the generalisation of the leading-order formulations to prescribed non-uniform rates of mass transfer and to three dimensions.

Recent research in whole-plant stomatal physiology, conducted largely with potted plants in controlled environments, suggests that stomatal conductance (gs) might be more closely linked to plant chemical variables than to hydraulic variables. To test this in a field situation, seasonal gs was examined in relation to a number of plant and environmental variables in 11 temperate, deciduous forest tree species. Stomatal conductance was generally better correlated with environmental variables (air temperature, vapor pressure deficit, PPFD) than with plant variables, and slightly better correlated with plant hydraulic variables (shoot water and osmotic potentials) than with plant chemical variables (xylem sap ABA concentration, xylem sap pH). We examined a model, developed previously for maize, which describes regulation of gs by xylem sap ABA concentration with leaf water status acting to modify stomatal sensitivity to the ABA signal. This model explained slightly more variation in seasonal gs in the forest trees than did single plant variables but not more variation than most single environmental variables. Response surface models, especially those incorporating environmental variables, were more consistently successful at explaining gs across species.