Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic

Obesity: A Biobehavioral Point of View

Excerpt: If you ask an overweight person, “Why are you fat?’, you will, almost invariably, get the answer, “Because 1 eat too much.” You will get this answer in spite of the fact that of thirteen studies, six find no significant differences in the caloric intake of obese versus nonobese subjects, five report that the obese eat significantly less than the nonobese, and only two report that they eat significantly more

Sport, physical activity and the establishment of Health and Wellbeing Boards in Nottingham and Nottinghamshire

This paper will examine the emergence of Health and Wellbeing Boards in Nottinghamshire and the City of Nottingham and explore the implications for sport and physical activity. At the time of writing the transfer of responsibilities for Public Health and the establishment of Health and Wellbeing Boards in both the City of Nottingham and within Nottinghamshire County Council are considered to be relatively advanced by the Strategic Health Authorities, the respective local authorities and by the boards of the two Primary Care Trusts. "Shadow"� Health and Well being Board have been established in both authorities and they have been meeting regularly for s everal months. Public health and commissioning staff have also been successfully relocated and new strategies and priorities are starting to emerge. Nottingham and Nottinghamshire have traditionally acknowledged the role of sport and physical activity to the wider determinants of public health and given a relatively high priority to the contribution that sport and physical activity can make to the ir preventative health and early intervention agendas. This paper will look at the transition to Health and Wellbeing boards to assess how the role of sport and physical activity may be changing and to identify opportunities for its contribution to policy and practise in the future. It will examine both the theory and practise behind the emerging governance arr angements, the strategic objectives and priorities, and the developing evidential base for future policy and delivery within the two areas

Impact of a Viscous Liquid Drop

We simulate the impact of a viscous liquid drop onto a smooth dry solid surface. As in experiments, when ambient air effects are negligible, impact flattens the falling drop without producing a splash. The no-slip boundary condition at the wall produces a boundary layer inside the liquid. Later, the flattening surface of the drop traces out the boundary layer. As a result, the eventual shape of the drop is a "pancake" of uniform thickness except at the rim, where surface tension effects are significant. The thickness of the pancake is simply the height where the drop surface first collides with the boundary layer.Comment: 5 pages, 3 figures, submitted to Physical Review Letter

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Regional-Specific Effects of Ovarian Hormone Loss on Synaptic Plasticity in Adult Human APOE Targeted Replacement Mice

The human apolipoprotein ε4 allele (APOE4) has been implicated as one of the strongest genetic risk factors associated with Alzheimer’s disease (AD) and in influencing normal cognitive functioning. Previous studies have demonstrated that mice expressing human apoE4 display deficits in behavioral and neurophysiological outcomes compared to those with apoE3. Ovarian hormones have also been shown to be important in modulating synaptic processes underlying cognitive function, yet little is known about how their effects are influenced by apoE. In the current study, female adult human APOE targeted replacement (TR) mice were utilized to examine the effects of human APOE genotype and long-term ovarian hormone loss on synaptic plasticity in limbic regions by measuring dendritic spine density and electrophysiological function. No significant genotype differences were observed on any outcomes within intact mice. However, there was a significant main effect of genotype on total spine density in apical dendrites in the hippocampus, with post-hoc t-tests revealing a significant reduction in spine density in apoE3 ovariectomized (OVX) mice compared to sham operated mice. There was also a significant main effect of OVX on the magnitude of LTP, with post-hoc t-tests revealing a decrease in apoE3 OVX mice relative to sham. In contrast, apoE4 OVX mice showed increased synaptic activity relative to sham. In the lateral amygdala, there was a significant increase in total spine density in apoE4 OVX mice relative to sham. This increase in spine density was consistent with a significant increase in spontaneous excitatory activity in apoE4 OVX mice. These findings suggest that ovarian hormones differentially modulate synaptic integrity in an apoE-dependent manner within brain regions that are susceptible to neurophysiological dysfunction associated with AD

Presupernova Evolution of Rotating Massive Stars I: Numerical Method and Evolution of the Internal Stellar Structure

The evolution of rotating stars with zero-age main sequence (ZAMS) masses in the range 8 to 25 M_sun is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70 % of break-up. Redistribution of angular momentum and chemical species are then followed as a consequence of rotationally induced circulation and instablities. The effects of the centrifugal force on the stellar structure are included. Uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (non-magnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlaying material of 1E16...1E17 erg s. These values are insensitive to the initial angular momentum. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to break-up. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.Comment: 62 pages, including 7 tables and 19 figures. Accepted by Ap

Searching for star-planet magnetic interaction in CoRoT observations

Close-in massive planets interact with their host stars through tidal and magnetic mechanisms. In this paper, we review circumstantial evidence for star-planet interaction as revealed by the photospheric magnetic activity in some of the CoRoT planet-hosting stars, notably CoRoT-2, CoRoT-4, and CoRoT-6. The phenomena are discussed in the general framework of activity-induced features in stars accompanied by hot Jupiters. The theoretical mechanisms proposed to explain the activity enhancements possibly related with hot Jupiter are also briefly reviewed with an emphasis on the possible effects at photospheric level. The unique advantages of CoRoT and Kepler observations to test these models are pointed out.Comment: Invited review paper accepted by Astrophysics and Space Science, 13 pages, 5 figure

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field