Mock-Gaussian Behaviour for Linear Statistics of Classical Compact Groups

We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is not. The precise number of Gaussian moments depends upon the particular statistic considered

Exact moments in a continuous time random walk with complete memory of its history

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.Comment: Revtex4, 10 pages, 2 figures. v2: applications discussed, clarity improved, corrected scaling of third momen

Persistence effects in deterministic diffusion

In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.Comment: 7 pages, 7 figure

Recruiting and retaining children and families' social workers. The potential of work discussion groups

Current difficulties with the recruitment and retention of children and families' social workers have been formally acknowledged. However, although initiatives which focus on remuneration and career progression are clearly welcome, research and evidence from practice highlights how social workers themselves place high value on the availability of good quality supervision. Yet, questions remain about whether first-line managers have the time or are even in the best position to offer this support. This article draws on the experience and evaluation of one particular model of supervision — 'work discussion groups' —and explores its impact with residential social work staff and teachers as well as the potential for further developments of this kind

The shape and pace of change in the electricity transition: sectoral dynamics and indicators of progress

Change is not linear. Time and again, industries, policymakers, and commentators in markets, technologies, and societies. This report outlines the potential dynamics of the transition to net-zero emissions; explains the general principles, characteristics, and common drivers of growth of emerging technologies; and explores progress against metrics of transition in electricity generation. Given that rapid technological progress and diffusion of zero-carbon technologies are critical to reduce emissions at the pace and scale required, this report looks at the deployment levels and rates of change needed to achieve global climate goals, assuming the widely observed “S-curve” and pace of change. The electricity sector has to lead the global transition required to avoid dangerous climate change. Meeting the goal of limiting warming to 1.5°C, as set out in the Paris Agreement, requires global power sector 1 Namely: “Holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C.” (UN, 2015). CO2 emissions to reach net zero before 2050, with most studies showing that solar and wind are likely to become dominant sources of zero-carbon power. Many assessments of deployment levels to date are very pessimistic, extrapolating linear growth and looking at the absolute contribution from renewable energy sources, which, though growing, is still limited. This report probes deeper and anchors its analysis in the more commonly observed nonlinear dynamics of technological transition, comparing the trends since 2010 with the pace of transition required. The results may surprise, and bring clarity to where progress is being made and where and how it needs to be pushed faster. A rapid transition is underway and appears now unstoppable, though its pace and depth will depend on policy. But inconsistency with dynamic indicators for fossil fuel-based generation points to a high risk of stranded fossil fuel generation assets irrespective of future policy decisions

The Effects of Post-Grazing Sward Conditions on Herbage Accumulation in Winter and Spring

Two on-farm experiments were conducted in the winter and spring of 1998 on a New Zealand seasonal production dairy farm to determine the effect of herbage mass present after grazing on subsequent pasture growth rates. Experiments involved a range of post-grazing levels of herbage mass (870, 1140, 1390, 1640, 1920 kg DM/ha in winter, and 1100, 1420, 1700 and 1910 kg DM/ha in spring) representing a range in cow intakes of 6.1-20.0 and 7.6-18.5 kg DM/cow/day in winter and spring, respectively. In both experiments there was a range of postgrazing herbage mass (1200-1600 kg DM/ha in winter and 1400-1800 kg DM/ha in spring) over which post-grazing residuals had little effect on pasture growth rates. This lack of response was explained by underlying changes in sward components. Grazing residuals of 1200-1300 and 1500-1600 kg DM/ha were recommended to provide an adequate compromise between the pasture and animal requirements of grazing management considered important in winter and spring respectively. This study adds to the growing evidence to support farming systems focused on sward targets in enhancing both pasture and animal performance