11,375 research outputs found
Global convergence analysis for the NIC flow
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
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
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
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
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?
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
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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