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We consider planar flow involving two viscous fluids in a porous medium. One fluid is injected through a line source at the origin and moves radially outwards, pushing the second, ambient fluid outwards. There is an interface between the two fluids and if the inner injected fluid is of lower viscosity, the interface is unstable to small disturbances and radially directed unstable Saffman–Taylor fingers are produced. A linearized theory is presented and is compared with nonlinear results obtained using a numerical spectral method. An additional theory is also discussed, in which the sharp interface is replaced with a narrow diffuse interfacial region. We show that the nonlinear results are in close agreement with the linearized theory for small-amplitude disturbances at early times, but that large-amplitude fingers develop at later times and can even detach completely from the initial injection region. [ABSTRACT FROM AUTHOR]

A viscous fluid is confined between two smooth horizontal walls, in a vertical channel. The upper wall may move with constant speed, but the lower wall is stationary and a portion of it is heated. A plume of heated fluid develops, and may also be swept downstream by the motion of the upper wall. When the heating effect is small and the upper plate does not move, a closed-form solution for the temperature profile is presented. A numerical spectral method is then presented, and allows highly accurate nonlinear solutions to be obtained, for the temperature and the fluid motion. These are compared against the closed-form solution in the linearized case, and the effects of nonlinearity on temperature and velocity are revealed. The results also show that periodic plume shedding from the heated region can occur in the nonlinear case. [ABSTRACT FROM AUTHOR]

Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here. [ABSTRACT FROM AUTHOR]

We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated. [ABSTRACT FROM AUTHOR]

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. [ABSTRACT FROM AUTHOR]

Background: There is evidence for the cost-effectiveness of health visitor (HV) training to assess postnatal depression (PND) and deliver psychological approaches to women at risk of depression. Whether this approach is cost-effective for lower-risk women is unknown. There is a need to know the cost of HV-delivered universal provision, and how much it might cost to improve health-related quality of life for postnatal women. A sub-study of a cluster-randomised controlled trial in the former Trent region (England) previously investigated the effectiveness of PoNDER HV training in mothers at lower risk of PND. We conducted a parallel cost-effectiveness analysis at 6-months postnatal for all mothers with lower-risk status attributed to an Edinburgh Postnatal Depression Scale (EPDS) score <12 at 6-weeks postnatal. Methods: Intervention HVs were trained in assessment and cognitive behavioural or person-centred psychological support techniques to prevent depression. Outcomes examined: quality-adjusted life-year (QALY) gains over the period between 6 weeks and 6 months derived from SF-6D (from SF-36); risk-of-depression at 6 months (dichotomising 6-month EPDS scores into lower risk (<12) and at-risk (⩾12). Results: In lower-risk women, 1474 intervention (63 clusters) and 767 control participants (37 clusters) had valid 6-week and 6-month EPDS scores. Costs and outcomes data were available for 1459 participants. 6-month adjusted costs were £82 lower in intervention than control groups, with 0.002 additional QALY gained. The probability of cost-effectiveness at £20 000 was very high (99%). Conclusions: PoNDER HV training was highly cost-effective in preventing symptoms of PND in a population of lower-risk women and cost-reducing over 6 months. [ABSTRACT FROM AUTHOR]

Background: Child and adolescent mental health disorders are present in around 10% of the population. Research indicates that many young people possess negative attitudes towards mental health difficulties among peers.Aims: To assess the impact of a mental health teaching programme on adolescent pupils' understanding.Method: Two-group pre-test-post-test control group study in two English secondary schools. Experimental classes (School E) received a six-lesson teaching intervention on mental health; control classes (School C) did not. Participants were 14- and 15-year-old pupils. The intervention consisted of six lessons on mental health issues common to young people: stress; depression; suicide/self-harm; eating disorders; being bullied; and intellectual disability. School C was given access to these lesson plans and materials on completion of the study. Understanding was measured at two time points, Time 1 (T(1)) and Time 2 (T(2)), 8 months apart, by a Mental Health Questionnaire. Behavioural, emotional and relationship strengths and difficulties were measured by the self-rated Strengths and Difficulties Questionnaire (SDQ) with five subscales: hyperactivity, emotional symptoms, conduct problems, peer problems and prosocial behaviour.Results: At T(2), pupils in School E compared with those in School C showed significantly more sensitivity and empathy towards people with mental health difficulties. They also used significantly fewer pejorative expressions to describe mental health difficulties. There was a significant reduction in SDQ scores on conduct problems and a significant increase on prosocial behaviour among School E pupils compared with controls. Pupils valued the intervention highly, in particular the lessons on suicide/self-harm.Conclusions: Teaching 14- and 15-year-olds about mental health difficulties helps to reduce stigma by increasing knowledge and promoting positive attitudes. The intervention also reduced self-reported conduct problems and increased prosocial behaviour. Generally, participating pupils were positive about the importance of lessons on mental health, and said that they had learnt much about the lesson topics. [ABSTRACT FROM AUTHOR]

Objective: Parents food choices and weight, but little is known about the social class distribution of parent self-reported child-feeding behaviours in two socio-economically contrasting areas.Design: A cross-sectional survey using the Parental Feeding Style Questionnaire. Mean scores were calculated for five child-feeding behaviours: control over eating, emotional feeding, encouragement/prompting, instrumental feeding and restriction. Parents behaviours that might be used to directly influence children's food intake and weight.Conclusions: Child-feeding behaviours differ between areas within a single city and within a largely white population, and this distribution is related to socio-economic and educational factors. Experimental and longitudinal studies are needed to further investigate the potential role of child-feeding behaviours in childhood overweight and obesity. [ABSTRACT FROM AUTHOR]