11,375 research outputs found

    Global convergence analysis for the NIC flow

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    Previously, a family of fast subspace tracking algorithms based on a novel information criterion (NIC) has been proposed and investigated. It is known that these new algorithms are associated with a new kind of flow, which is called the NIC flow in this paper as in the case of the conventional Oja subspace algorithms with the Oja flow. In this paper, some fundamental questions about this new NIC flow such as its solution existence and convergence, are investigated. In addition, the convergence domain is characterized. Some important results on these issues are obtained via manifold theor

    Numerical Simulations of Driven Relativistic MHD Turbulence

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    A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.Comment: Accepted to Ap

    Simulating Supersonic Turbulence in Magnetized Molecular Clouds

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    We present results of large-scale three-dimensional simulations of weakly magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our numerical experiments are carried out with the Piecewise Parabolic Method on a Local Stencil and assume an isothermal equation of state. The turbulence is driven by a large-scale isotropic solenoidal force in a periodic computational domain and fully develops in a few flow crossing times. We then evolve the flow for a number of flow crossing times and analyze various statistical properties of the saturated turbulent state. We show that the energy transfer rate in the inertial range of scales is surprisingly close to a constant, indicating that Kolmogorov's phenomenology for incompressible turbulence can be extended to magnetized supersonic flows. We also discuss numerical dissipation effects and convergence of different turbulence diagnostics as grid resolution refines from 256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC 2009 conferenc

    Dynamical stability of a thermally stratified intracluster medium with anisotropic momentum and heat transport

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    In weakly-collisional plasmas such as the intracluster medium (ICM), heat and momentum transport become anisotropic with respect to the local magnetic field direction. Anisotropic heat conduction causes the slow magnetosonic wave to become buoyantly unstable to the magnetothermal instability (MTI) when the temperature increases in the direction of gravity and to the heat-flux--driven buoyancy instability (HBI) when the temperature decreases in the direction of gravity. The local changes in magnetic field strength that attend these instabilities cause pressure anisotropies that viscously damp motions parallel to the magnetic field. In this paper we employ a linear stability analysis to elucidate the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy) on the MTI and HBI. By stifling the convergence/divergence of magnetic field lines, pressure anisotropy significantly affects how the ICM interacts with the temperature gradient. Instabilities which depend upon the convergence/divergence of magnetic field lines to generate unstable buoyant motions (the HBI) are suppressed over much of the wavenumber space, whereas those which are otherwise impeded by field-line convergence/divergence (the MTI) are strengthened. As a result, the wavenumbers at which the HBI survives largely unsuppressed in the ICM have parallel components too small to rigorously be considered local. This is particularly true as the magnetic field becomes more and more orthogonal to the temperature gradient. In contrast, the fastest-growing MTI modes are unaffected by anisotropic viscosity. However, we find that anisotropic viscosity couples slow and Alfven waves in such a way as to buoyantly destabilise Alfvenic fluctuations when the temperature increases in the direction of gravity. Consequently, many wavenumbers previously considered MTI-stable or slow-growing are in fact maximally unstable. (abridged)Comment: 15 pages, 7 figures, accepted by MNRAS; typos fixed and minor corrections made; color figures available at http://www-thphys.physics.ox.ac.uk/people/kunz/Kunz11_colorfigs.pd

    Turbulence and Steady Flows in 3D Global Stratified MHD Simulations of Accretion Disks

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    We present full 2 Pi global 3-D stratified MHD simulations of accretion disks. We interpret our results in the context of proto-planetary disks. We investigate the turbulence driven by the magneto-rotational instability (MRI) using the PLUTO Godunov code in spherical coordinates with the accurate and robust HLLD Riemann solver. We follow the turbulence for more than 1500 orbits at the innermost radius of the domain to measure the overall strength of turbulent motions and the detailed accretion flow pattern. We find that regions within two scale heights of the midplane have a turbulent Mach number of about 0.1 and a magnetic pressure two to three orders of magnitude less than the gas pressure, while outside three scale heights the magnetic pressure equals or exceeds the gas pressure and the turbulence is transonic, leading to large density fluctuations. The strongest large-scale density disturbances are spiral density waves, and the strongest of these waves has m=5. No clear meridional circulation appears in the calculations because fluctuating radial pressure gradients lead to changes in the orbital frequency, comparable in importance to the stress gradients that drive the meridional flows in viscous models. The net mass flow rate is well-reproduced by a viscous model using the mean stress distribution taken from the MHD calculation. The strength of the mean turbulent magnetic field is inversely proportional to the radius, so the fields are approximately force-free on the largest scales. Consequently the accretion stress falls off as the inverse square of the radius.Comment: Accepted for publication in Ap

    Will the Explosive Growth of China Continue?

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    The role of China in the world economy is constantly growing. In particular we observe that it plays more and more important role in the support of theworld economic growth (as well as high prices of certain very important commodities). In the meantime the perspectives of the Chinese economy (as well as possible fates of the Chinese society) remain unclear, whereas respective forecasts look rather contradictory. That is why the search for new aspects and modes of analysis of possible development of China turns out to be rather important for the forecasting of global futures. This article employs a combination of scientific methods that imply (a) the analysis at the level of Chinese economic model; (b) the analysis at regional level (at this level the Chinese economic model is compared with the regional East Asian model); (c) the analysis at the global level that relies on the modified world-system approach that allows to answer the question whether China will replace the USA as the global leader. It is important that the analysis is conducted simultaneously in economic, social, demographic, and political dimensions. As regards the analysis of specific features of the Chinese model as an especial type of the East Asian model (that is based on the export orientation, capital & technology importation, as well as cheap labor force), we note as organic features of the Chinese model the totalitarian power of the Communist Party and the immenseness of resources. As regards special features of the Chinese model, we note (in addition to “cheap ecology” and cheap labor force) and emphasize that China has a multilevel (in a way unique) system of growth driving forces, where, as opposed to developed states, the dominant role belongs not to native private capital, but to state corporations, local authorities and foreign business. This explains the peculiarities of the Chinese investment (or rather overinvestment), which determines high growth rate up to a very significant degree. A unique feature of the Chinese model is the competition of provinces and territories for investments and high growth indicators. As regards perspectives of the global hegemony of China, we intend to demonstrate that, on the one hand, economic and political positions of China will strengthen in the forthcoming decades, but, on the other hand, China, assuming all possible future success, will be unable to take the USA position in the World System. We believe that in a direct connection with the development of globalization processes the hegemony cycle pattern is likely to come to its end, which will lead to the World System reconfiguration and the emergence of its new structure that will allow the World System to continue its further development without a hegemon. Finally, the article describes some possible scenarios of the development of China. We demonstrate that China could hardly avoid serious difficulties and critical situations (including those connected with demographic problems); however, there could be different scenarios of how China will deal with the forthcoming crisis. We also come to the conclusion that it would be better for China to achieve a slowdown to moderate growth rates (that would allow China to go through the forthcoming complex transition period with less losses) than to try to return at any cost to explosive growth rates attested in the 2000s

    Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow

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    The global-scale interior magnetic field needed to account for the Sun's observed differential rotation can be effective only if confined below the convection zone in all latitudes, including the polar caps. Axisymmetric nonlinear MHD solutions are obtained showing that such confinement can be brought about by a very weak downwelling flow U~10^{-5}cm/s over each pole. Such downwelling is consistent with the helioseismic evidence. All three components of the magnetic field decay exponentially with altitude across a thin "magnetic confinement layer" located at the bottom of the tachocline. With realistic parameter values, the thickness of the confinement layer ~10^{-3} of the Sun's radius. Alongside baroclinic effects and stable thermal stratification, the solutions take into account the stable compositional stratification of the helium settling layer, if present as in today's Sun, and the small diffusivity of helium through hydrogen, chi. The small value of chi relative to magnetic diffusivity produces a double boundary-layer structure in which a "helium sublayer" of smaller vertical scale is sandwiched between the top of the helium settling layer and the rest of the confinement layer. Solutions are obtained using both semi-analytical and purely numerical, finite-difference techniques. The confinement-layer flows are magnetostrophic to excellent approximation. More precisely, the principal force balances are between Lorentz, Coriolis, pressure-gradient and buoyancy forces, with relative accelerations and viscous forces negligible. This is despite the kinematic viscosity being somewhat greater than chi. We discuss how the confinement layers at each pole might fit into a global dynamical picture of the solar tachocline. That picture, in turn, suggests a new insight into the early Sun and into the longstanding enigma of solar lithium depletion.Comment: Accepted by JFM. 36 pages, 10 figure
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