125 research outputs found
Aspects of Density Fluctuations in Compressible MHD Turbulence
We study scaling relations of compressible isothermal strongly magnetized
turbulence using numerical simulations with resolution 512. We find a good
correspondence of our results with the Fleck (1996) model of compressible
hydrodynamic turbulence. In particular, we find that the density-weighted
velocity, i.e. , proposed in
Kritsuk et al. (2007) obeys the Kolmogorov scaling, i.e. for the high Mach number turbulence. Similarly, we find that the
exponents of the third order structure functions for stay
equal to unity for all Mach numbers studied. The scaling of higher order
correlations obeys the She-L\'{e}v\^{e}que (1994) scalings corresponding to the
two-dimensional dissipative structures, and this result does not change with
the Mach number either. In contrast to velocity which exhibits
different scaling parallel and perpendicular to the local magnetic field, the
scaling of is similar in both directions. In addition, we find
that the peaks of density create a hierarchy in which both physical and column
densities decrease with the scale in accordance to the Fleck (1996)
predictions. This hierarchy can be related ubiquitous small ionized and neutral
structures (SINS) in the interstellar gas. We believe that studies of
statistics of the column density peaks can provide both consistency check for
the turbulence velocity studies and insight into supersonic turbulence, when
the velocity information is not available.Comment: 10 pages, 7 figures, Proceeings for 6th Annual International
Astrophysics Conference, Honolulu, 200
Degree of Economic Freedom and Relationship to Economic Growth and Human Development
Presented in this article is an analysis of the relationship between the Index of Economic Freedom and indices of economic growth, i.e. GDP per capita and the Human Development Index. The McPherson coefficient of correlation was calculated from several different perspectives. Described in the final part of the article is the testing of the hypotheses, while a short commentary on the results obtained is also presented.liberalism, economic growth, index of economic freedom
Scaling Relations of Compressible MHD Turbulence
We study scaling relations of compressible strongly magnetized turbulence. We
find a good correspondence of our results with the Fleck (1996) model of
compressible hydrodynamic turbulence. In particular, we find that the
density-weighted velocity, i.e. , proposed in Kritsuk et
al. (2007) obeys the Kolmogorov scaling, i.e. for the
high Mach number turbulence. Similarly, we find that the exponents of the third
order structure functions for stay equal to unity for the all the Mach
numbers studied. The scaling of higher order correlations obeys the She-Leveque
(1994) scalings corresponding to the two-dimensional dissipative structures,
and this result does not change with the Mach number either. In contrast to
which exhibits different scaling parallel and perpendicular to the local
magnetic field, the scaling of is similar in both directions. In addition,
we find that the peaks of density create a hierarchy in which both physical and
column densities decrease with the scale in accordance to the Fleck (1996)
predictions. This hierarchy can be related ubiquitous small ionized and neutral
structures (SINS) in the interstellar gas. We believe that studies of
statistics of the column density peaks can provide both consistency check for
the turbulence velocity studies and insight into supersonic turbulence, when
the velocity information is not available.Comment: 4 pages, 5 figure
Particle Acceleration by Magnetic Reconnection
Observational data require a rich variety of mechanisms to accelerate fast
particles in astrophysical environments operating under different conditions.
The mechanisms discussed in the literature include varying magnetic fields in
compact sources, stochastic processes in turbulent environments, and
acceleration behind shocks. An alternative, much less explored mechanism
involves particle acceleration within magnetic reconnection sites. In this
chapter we discuss this mechanism and show that particles can be efficiently
accelerated by reconnection through a first order Fermi process within large
scale current sheets (specially when in the presence of local turbulence which
speeds up the reconnection and make the acceleration region thicker) and also
through a second order Fermi process in pure MHD turbulent environments.Comment: 24 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1103.2984, arXiv:1202.5256, arXiv:1008.1981 by other author
Cosmic ray driven dynamo in galactic disks. A parameter study
We present a parameter study of the magnetohydrodynamical dynamo driven by
cosmic rays in the interstellar medium (ISM) focusing on the efficiency of
magnetic field amplification and the issue of energy equipartition between
magnetic, kinetic and cosmic ray (CR) energies. We perform numerical CR-MHD
simulations of the ISM using the extended version of ZEUS-3D code in the
shearing box approximation and taking into account the presence of Ohmic
resistivity, tidal forces and vertical disk gravity. CRs are supplied in
randomly distributed supernova (SN) remnants and are described by the
diffusion-advection equation, which incorporates an anisotropic diffusion
tensor. The azimuthal magnetic flux and total magnetic energy are amplified
depending on a particular choice of model parameters. We find that the most
favorable conditions for magnetic field amplification correspond to magnetic
diffusivity of the order of 3\times 10^{25} \cm^2\s^{-1}, SN rates close to
those observed in the Milky Way, periodic SN activity corresponding to spiral
arms, and highly anisotropic and field-aligned CR diffusion. The rate of
magnetic field amplification is relatively insensitive to the magnitude of SN
rates in a rage of spanning 10% up to 100% of realistic values. The timescale
of magnetic field amplification in the most favorable conditions is 150 Myr, at
galactocentric radius equal to 5 kpc. The final magnetic field energies
fluctuate near equipartition with the gas kinetic energy. In all models CR
energy exceeds the equipartition values by a least an order of magnitude, in
contrary to the expected equipartition. We suggest that the excess of cosmic
rays can be attributed to the fact that the shearing-box does not permit cosmic
rays to leave the system along the horizontal magnetic field.Comment: 12 papges, 11 figures, accepted for publication in Astronomy and
Astrophysic
Studies of regular and random magnetic fields in the ISM: statistics of polarization vectors and the Chandrasekhar-Fermi technique
Polarimetry is extensively used as a tool to trace the interstellar magnetic
field projected on the plane of sky. Moreover, it is also possible to estimate
the magnetic field intensity from polarimetric maps based on the
Chandrasekhar-Fermi method. In this work, we present results for turbulent,
isothermal, 3-D simulations of sub/supersonic and sub/super-Alfvenic cases.
With the cubes, assuming perfect grain alignment, we created synthetic
polarimetric maps for different orientations of the mean magnetic field with
respect to the line of sight (LOS). We show that the dispersion of the
polarization angle depends on the angle of the mean magnetic field regarding
the LOS and on the Alfvenic Mach number. However, the second order structure
function of the polarization angle follows the relation , being dependent exclusively on the Alfvenic Mach number.
The results show an anti-correlation between the polarization degree and the
column density, with exponent , in agreement with
observations, which is explained by the increase in the dispersion of the
polarization angle along the LOS within denser regions. However, this effect
was observed exclusively on supersonic, but sub-Alfvenic, simulations. For the
super-Alfvenic, and the subsonic model, the polarization degree showed to be
intependent on the column density. Our major quantitative result is a
generalized equation for the CF method, which allowed us to determine the
magnetic field strength from the polarization maps with errors . We also
account for the role of observational resolution on the CF method.Comment: submitted to ApJ, 42 page
Reconnection Studies Under Different Types of Turbulence Driving
We study a model of fast magnetic reconnection in the presence of weak
turbulence proposed by Lazarian and Vishniac (1999) using three-dimensional
direct numerical simulations. The model has been already successfully tested in
Kowal et al. (2009) confirming the dependencies of the reconnection speed
on the turbulence injection power and the injection scale
expressed by a constraint
and no observed dependency on Ohmic resistivity. In Kowal et al. (2009), in
order to drive turbulence, we injected velocity fluctuations in Fourier space
with frequencies concentrated around , as described in
Alvelius (1999). In this paper we extend our previous studies by comparing fast
magnetic reconnection under different mechanisms of turbulence injection by
introducing a new way of turbulence driving. The new method injects velocity or
magnetic eddies with a specified amplitude and scale in random locations
directly in real space. We provide exact relations between the eddy parameters
and turbulent power and injection scale. We performed simulations with new
forcing in order to study turbulent power and injection scale dependencies. The
results show no discrepancy between models with two different methods of
turbulence driving exposing the same scalings in both cases. This is in
agreement with the Lazarian and Vishniac (1999) predictions. In addition, we
performed a series of models with varying viscosity . Although Lazarian
and Vishniac (1999) do not provide any prediction for this dependence, we
report a weak relation between the reconnection speed with viscosity,
.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with
arXiv:0903.205
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