20,394 research outputs found
A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets
We propose two sets of initial conditions for magnetohydrodynamics (MHD) in
which both the velocity and the magnetic fields have spatial symmetries that
are preserved by the dynamical equations as the system evolves. When
implemented numerically they allow for substantial savings in CPU time and
memory storage requirements for a given resolved scale separation. Basic
properties of these Taylor-Green flows generalized to MHD are given, and the
ideal non-dissipative case is studied up to the equivalent of 2048^3 grid
points for one of these flows. The temporal evolution of the logarithmic
decrements, delta, of the energy spectrum remains exponential at the highest
spatial resolution considered, for which an acceleration is observed briefly
before the grid resolution is reached. Up to the end of the exponential decay
of delta, the behavior is consistent with a regular flow with no appearance of
a singularity. The subsequent short acceleration in the formation of small
magnetic scales can be associated with a near collision of two current sheets
driven together by magnetic pressure. It leads to strong gradients with a fast
rotation of the direction of the magnetic field, a feature also observed in the
solar wind.Comment: 8 pages, 4 figure
Research on processes for utilization of lunar resources quarterly report, 16 jul. - 15 oct. 1964
Lunar resource utilization - silicate reduction unit and carbon monoxide reduction reacto
Investigation of the fiber reinforcement of a cobalt base alloy for application at elevated temperature
Technique developed for incorporating alumina and silicon carbide fibers in cobalt base alloy for application at high temperature
Hypothesis Testing For Network Data in Functional Neuroimaging
In recent years, it has become common practice in neuroscience to use
networks to summarize relational information in a set of measurements,
typically assumed to be reflective of either functional or structural
relationships between regions of interest in the brain. One of the most basic
tasks of interest in the analysis of such data is the testing of hypotheses, in
answer to questions such as "Is there a difference between the networks of
these two groups of subjects?" In the classical setting, where the unit of
interest is a scalar or a vector, such questions are answered through the use
of familiar two-sample testing strategies. Networks, however, are not Euclidean
objects, and hence classical methods do not directly apply. We address this
challenge by drawing on concepts and techniques from geometry, and
high-dimensional statistical inference. Our work is based on a precise
geometric characterization of the space of graph Laplacian matrices and a
nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate
our resulting methodologies for testing in the context of networks derived from
functional neuroimaging data on human subjects from the 1000 Functional
Connectomes Project. In particular, we show that this global test is more
statistical powerful, than a mass-univariate approach. In addition, we have
also provided a method for visualizing the individual contribution of each edge
to the overall test statistic.Comment: 34 pages. 5 figure
Investigation of sputtering effects on the moon's surface Eleventh quarterly status report, 25 Oct. 1965 - 24 Jan. 1966
Implications of Lunar 9 moon probe, sputtering yield reduction due to surface roughness, water formation by solar wind bombardment, photometric function of moon, and chemical sputterin
A comparison of spectral element and finite difference methods using statically refined nonconforming grids for the MHD island coalescence instability problem
A recently developed spectral-element adaptive refinement incompressible
magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp.
Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island
coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD
process that can produce sharp current layers and subsequent reconnection and
heating in a high-Lundquist number plasma such as the solar corona [Ng and
Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin
current layers, it is highly desirable to use adaptively or statically refined
grids to resolve them, and to maintain accuracy at the same time. The output of
the spectral-element static adaptive refinement simulations are compared with
simulations using a finite difference method on the same refinement grids, and
both methods are compared to pseudo-spectral simulations with uniform grids as
baselines. It is shown that with the statically refined grids roughly scaling
linearly with effective resolution, spectral element runs can maintain accuracy
significantly higher than that of the finite difference runs, in some cases
achieving close to full spectral accuracy.Comment: 19 pages, 17 figures, submitted to Astrophys. J. Supp
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
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