Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B_p^2/2\mu_0) \tau_{\rm corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.Comment: 16 pages, 8 figure

Assessing the quality of life of children with sickle cell anaemia using self-, parent-proxy and healthcare professional-proxy reports

Objectives The quality of life (QoL) of children with sickle cell anaemia (SCA) in the United Kingdom has not been examined, and a discrepancy measure based on Gap theory has rarely been used. This study investigated whether (1) child self-reports of QoL using a discrepancy measure (the Generic Children's QoL Measure; GCQ) are lower than those from healthy children, (2) proxy reports from parents and health care professionals are lower than child self-reports, and (3) demographic and disease severity indicators are related to QoL. Design and methods An interdependent groups, cross-sectional design was implemented. Seventy-four children with SCA, their parent, and members of their health care team completed the GCQ. Demographic and disease severity indicators were recorded. GCQ data from healthy children were obtained from the UK Data Archive. Results Contrary to past research, when examining generic discrepancy QoL, children with SCA did not report a lower QoL than healthy children, and parent- and health care professional-proxy reports were not lower than child self-reports. Few of the demographic and disease severity indicators were related to QoL. Conclusions Proxy reports may be used to gain a more complete picture of QoL, but should not be a substitute for self-reports. The explanation for the relatively high levels of QoL reported is not clear, but children with SCA may have realistic expectations about their ideal-self, place greater emphasis on aspects other than health in shaping their QoL, and define achievements within the limits of their illness. Future research should focus on psychological factors in explaining QoL

The Nusselt numbers of horizontal convection

We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $\kappa$ is the molecular diffusivity of buoyancy $b$. This connection between $\mathbf{J}$ and $\kappa\langle|\boldsymbol{\nabla}b|^2\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $\kappa \langle|\boldsymbol{\nabla}b|^2\rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $\kappa\langle|\boldsymbol{\nabla} b|^2\rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent "surface Nusselt number", defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{\rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|\mathbf{\nabla}b|^2$ demanded by $\kappa\langle|\mathbf{\nabla}b|^2\rangle$.Comment: 16 pages, 7 figure

A qualitative exploration of health-related quality of life and health behaviours in children with sickle cell disease and healthy siblings

Objectives This study explored the health-related quality of life (HRQL) and health behaviours of children with sickle cell disease (SCD) and healthy siblings, drawing on Gap theory, which suggests HRQL is the discrepancy between current and ideal selves. Design Thirty-two interviews, facilitated by children’s drawings of their current and ideal selves were thematically analysed. Results Two themes were identified. First, limitations of SCD and adjusted expectations. Children with SCD report some discrepancy in HRQL as they would like to participate in more physical activity, but overall, they appear to have normalised their condition and adjusted their expectations in the context of the limits of their condition. Healthy siblings worry about their sibling and have greater expectations about engaging in adventurous activities and for their future. Second, coping with SCD. Children have limited social support, although children with SCD seek support from their mothers. They also modify health behaviours, like reducing exercise to help prevent and cope with sickle-related pain. Conclusion Children have some discrepancies in their HRQL but adjusted expectations among children with SCD may reduce discrepancy. Adapting health behaviours may help to cope with SCD but it is important that reductions in physical activity do not impair HRQL

Dynamical screening effects in hot-electron scattering from electron-hole plasma and LO-phonon modes in quantum wires

Cataloged from PDF version of article.We present a fully dynamical and finite temperature study of the hot-electron momentum relaxation rate and the power loss in a coupled system of electron-hole plasma and bulk LO-phonons in a quantum wire structure. Interactions of the scattered electron with neutral plasma components and phonons are treated on an equal footing within the random-phase approximation. Coupled mode effects substantially change the transport properties of the system at low temperatures. Particularly, the ''plasmon-like'' and ''LO-phonon-like'' excitations yield comparable rates which, as a consequence of the singular nature of the 1D density of states, can be large at the threshold. This is in contrast to room temperature results where only the LO-phonon mode contributes significantly to the rate. The density and temperature dependence of the power loss reveals that dynamical screening effects are important, and energy-momentum conservation cannot be satisfied above a certain density for a given initial energy. Copyright (C) 1996 Elsevier Science Lt

The APR equation of state for simulations of supernovae, neutron stars and binary mergers

Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multi-messenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in which parameters of the interaction are fit to reproduce the energy density of nuclear matter and/or properties of heavy nuclei, the EOS of APR is obtained from potentials resulting from fits to nucleon-nucleon scattering and properties of light nuclei. In addition, this EOS features a phase transition to a neutral pion condensate at supra-nuclear densities. We show that differences in the effective masses between EOSs have consequences for the properties of nuclei in the sub-nuclear inhomogeneous phase of matter. We also test the new EOS of APR in spherically symmetric core-collapse of massive stars with $15M_\odot$ and $40M_\odot$, respectively. We find that the phase transition in the EOS of APR speeds up the collapse of the star. However, this phase transition does not generate a second shock wave or another neutrino burst as reported for the hadron-to-quark phase transition. The reason for this difference is that the onset of the phase transition in the EOS of APR occurs at larger densities than for the quark-to-hadron transition employed earlier which results in a significantly smaller softening of the high density EOS.Comment: 35 pages, 17 figures, 5 table

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion -- a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.Comment: 4 pages, 3 figure