Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Longitudinal study of changes in body mass index, anthropometric measures, dietary intake and physical activity in cohorts of school-going Irish adolescents

The prevalence of obesity worldwide has increased dramatically over the last few decades. Poor dietary habits and low levels of exercise in adolescence are often maintained into adulthood where they can impact on the incidence of obesity and chronic diseases. A 3-year longitudinal study of anthropometric, dietary and exercise parameters was carried out annually (2005 - 2007) in 3 Irish secondary schools. Anthropometric measurements were taken in each year and analysed longitudinally. Overweight and obesity were at relatively low levels in these adolescents. Height, weight, BMI, waist and hip circumferences and TST increased significantly over the 3 years. Waist-to-hip ratio (WHR) decreased significantly over time. Boys were significantly taller than girls across the 3 years. A 3-day weighed food diary was used to assess food intake by the adolescents. Analysis of dietary intake data was determined using WISP©. Mean daily energy and nutrient intakes were reported. Mean daily energy and macronutrient intakes were analysed longitudinally. The adolescents’ diet was characterised by relatively high saturated fat intakes and insufficient fruit and vegetable consumption. The dietary pattern did not change significantly over the 3 years. Boys consumed more energy than girls over the study period. A validated questionnaire was used to assess physical activity and sedentary activity levels. Boys were substantially more active and had higher energy expenditure estimates than girls throughout the study. A significant longitudinal decrease in physical activity levels among the adolescents was observed. Both genders spent more than the recommended amount of time (hrs/day) pursing sedentary activities. The dietary pattern in these Irish adolescents is relatively poor. Of additional concern is the overall longitudinal decrease in physical activity levels. Promoting consumption of a balanced diet and increased exercise levels among adolescents will help to reduce future public health care costs due to weight-related diseases.

Supercapattery based on binder-free Co3 (PO4)2·8H2O multilayer nano/microflakes on nickel foam

A binder-free cobalt phosphate hydrate (Co3(PO4)2·8H2O) multilayer nano/microflake structure is synthesized on nickel foam (NF) via a facile hydrothermal process. Four different concentrations (2.5, 5, 10, and 20 mM) of Co2+ and PO4–3 were used to obtain different mass loading of cobalt phosphate on the nickel foam. The Co3(PO4)2·8H2O modified NF electrode (2.5 mM) shows a maximum specific capacity of 868.3 C g–1 (capacitance of 1578.7 F g–1) at a current density of 5 mA cm–2 and remains as high as 566.3 C g–1 (1029.5 F g–1) at 50 mA cm–2 in 1 M NaOH. A supercapattery assembled using Co3(PO4)2·8H2O/NF as the positive electrode and activated carbon/NF as the negative electrode delivers a gravimetric capacitance of 111.2 F g–1 (volumetric capacitance of 4.44 F cm–3). Furthermore, the device offers a high specific energy of 29.29 Wh kg–1 (energy density of 1.17 mWh cm–3) and a specific power of 4687 W kg–1 (power density of 187.5 mW cm–3).