614 research outputs found
The role of parametric instabilities in turbulence generation and proton heating: Hybrid simulations of parallel propagating Alfv\'en waves
Large amplitude Alfv\'en waves tend to be unstable to parametric
instabilities which result in a decay process of the initial wave into
different daughter waves depending upon the amplitude of the fluctuations and
the plasma beta. The propagation angle with respect to the mean magnetic field
of the daughter waves plays an important role in determining the type of decay.
In this paper, we revisit this problem by means of multi-dimensional hybrid
simulations. In particular, we study the decay and the subsequent nonlinear
evolution of large-amplitude Alfv\'en waves by investigating the saturation
mechanism of the instability and its final nonlinear state reached for
different wave amplitudes and plasma beta conditions. As opposed to
one-dimensional simulations where the Decay instability is suppressed for
increasing plasma beta values, we find that the decay process in
multi-dimensions persists at large values of the plasma beta via the
filamentation/magnetosonic decay instabilities. In general, the decay process
acts as a trigger both to develop a perpendicular turbulent cascade and to
enhance mean field-aligned wave-particle interactions. We find indeed that the
saturated state is characterized by a turbulent plasma displaying a
field-aligned beam at the Alfv\'en speed and increased temperatures that we
ascribe to the Landau resonance and pitch angle scattering in phase space
Testing Conditional Independence of Discrete Distributions
We study the problem of testing \emph{conditional independence} for discrete
distributions. Specifically, given samples from a discrete random variable on domain , we want to distinguish,
with probability at least , between the case that and are
conditionally independent given from the case that is
-far, in -distance, from every distribution that has this
property. Conditional independence is a concept of central importance in
probability and statistics with a range of applications in various scientific
domains. As such, the statistical task of testing conditional independence has
been extensively studied in various forms within the statistics and
econometrics communities for nearly a century. Perhaps surprisingly, this
problem has not been previously considered in the framework of distribution
property testing and in particular no tester with sublinear sample complexity
is known, even for the important special case that the domains of and
are binary.
The main algorithmic result of this work is the first conditional
independence tester with {\em sublinear} sample complexity for discrete
distributions over . To complement our upper
bounds, we prove information-theoretic lower bounds establishing that the
sample complexity of our algorithm is optimal, up to constant factors, for a
number of settings. Specifically, for the prototypical setting when , we show that the sample complexity of testing conditional
independence (upper bound and matching lower bound) is
\[
\Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,.
\
Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers
We investigate properties of the scale dependence and cross-scale transfer of
kinetic energy in compressible three-dimensional hydrodynamic turbulence, by
means of two direct numerical simulations of decaying turbulence with initial
Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~
100. The turbulent dynamics is analyzed using compressible and incompressible
versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin
(KHM) equations. We find that the nonlinear coupling leads to a flux of the
kinetic energy to small scales where it is dissipated; at the same time, the
reversible pressure-dilatation mechanism causes oscillatory exchanges between
the kinetic and internal energies with an average zero net energy transfer.
While the incompressible KHM and ST equations are not generally valid in the
simulations, their compressible counterparts are well satisfied and describe,
in a quantitatively similar way, the decay of the kinetic energy on large
scales, the cross-scale energy transfer/cascade, the pressure dilatation, and
the dissipation. There exists a simple relationship between the KHM and ST
results through the inverse proportionality between the wave vector k and the
spatial separation length l as k l ~ 3^1/2. For a given time the dissipation
and pressure-dilatation terms are strong on large scales in the KHM approach
whereas the ST terms become dominant on small scales; this is owing to the
complementary cumulative behavior of the two methods. The effect of pressure
dilatation is weak when averaged over a period of its oscillations and may lead
to a transfer of the kinetic energy from large to small scales without a net
exchange between the kinetic and internal energies. Our results suggest that
for large-enough systems there exists an inertial range for the kinetic energy
cascade ...Comment: 14 pages, 10 figure
Recent Decisions
CHOICE OF LAW--WRONGFUL DEATH--GOVERNMENTAL-INTEREST ANALYSIS DETERMINES LAW APPLICABLE TO MEASURE OF DAMAGES IN CLAIMS ARISING FROM FOREIGN Air CRASH
John Edison Drake
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EUROPEAN COMMUNITIES--FREE MOVEMENT OF WORKERS--COURT OF JUSTICE SETS GUIDELINES FOR USE BY MEMBER STATES OF THE PUBLIC POLICY EXCEPTION IN ARTICLE 48
Heidi A. Rohrbach
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TAX TREATIES--UNITED STATES MAY USE THE INTERNAL REVENUE CODE SUMMONING AUTHORITY TO OBTAIN DOMESTIC INFORMATION SOLELY TO AID A FOREIGN DOMESTIC TAX INVESTIGATION PURSUANT TO A TAX TREATY
John R. Hellinger
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TREATY INTERPRETATION--WARSAW CONVENTION-- PASSENGERS UNDERGOING SEARCH PREREQUISITE TO BOARDING ARE ENGAGED IN OPERATIONS OF EMBARKING
Elizabeth Graeme Brownin
Plasma turbulence and kinetic instabilities at ion scales in the expanding solar wind
The relationship between a decaying strong turbulence and kinetic instabilities in a slowly expanding plasma is investigated using two-dimensional (2D) hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations that have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops; magnetic field fluctuations exhibit a power-law spectrum at large scales and a steeper spectrum at ion scales. The turbulent cascade leads to an overall anisotropic proton heating, protons are heated in the perpendicular direction, and, initially, also in the parallel direction. The imposed expansion leads to generation of a large parallel proton temperature anisotropy which is at later stages partly reduced by turbulence. The turbulent heating is not sufficient to overcome the expansion-driven perpendicular cooling and the system eventually drives the oblique firehose instability in a form of localized nonlinear wave packets which efficiently reduce the parallel temperature anisotropy. This work demonstrates that kinetic instabilities may coexist with strong plasma turbulence even in a constrained 2D regime
The oblique firehose instability in a bi-kappa magnetized plasma
In this work, we derive a dispersion equation that describes the excitation
of the oblique (or Alfv\'en) firehose instability in a plasma that contains
both electron and ion species modelled by bi-kappa velocity distribution
functions. The equation is obtained with the assumptions of low-frequency waves
and moderate to large values of the parallel (respective to the ambient
magnetic field) plasma beta parameter, but it is valid for any direction of
propagation and for any value of the particle gyroradius (or Larmor radius).
Considering values for the physical parameters typical to those found in the
solar wind, some solutions of the dispersion equation, corresponding to the
unstable mode, are presented. In order to implement the dispersion solver,
several new mathematical properties of the special functions occurring in a
kappa plasma are derived and included. The results presented here suggest that
the superthermal characteristic of the distribution functions leads to
reductions to both the maximum growth rate of the instability and of the
spectral range of its occurrence
Nonlinear theory of mirror instability near threshold
An asymptotic model based on a reductive perturbative expansion of the drift
kinetic and the Maxwell equations is used to demonstrate that, near the
instability threshold, the nonlinear dynamics of mirror modes in a magnetized
plasma with anisotropic ion temperatures involves a subcritical
bifurcation,leading to the formation of small-scale structures with amplitudes
comparable with the ambient magnetic field
Magnetic field turbulence in the solar wind at sub-ion scales: in situ observations and numerical simulations
We investigate the transition of the solar wind turbulent cascade from MHD to
sub-ion range by means of a detail comparison between in situ observations and
hybrid numerical simulations. In particular we focus on the properties of the
magnetic field and its component anisotropy in Cluster measurements and hybrid
2D simulations. First, we address the angular distribution of wave-vectors in
the kinetic range between ion and electron scales by studying the variance
anisotropy of the magnetic field components. When taking into account the
single-direction sampling performed by spacecraft in the solar wind, the main
properties of the fluctuations observed in situ are also recovered in our
numerical description. This result confirms that solar wind turbulence in the
sub-ion range is characterized by a quasi-2D gyrotropic distribution of
k-vectors around the mean field. We then consider the magnetic compressibility
associated with the turbulent cascade and its evolution from large-MHD to
sub-ion scales. The ratio of field-aligned to perpendicular fluctuations,
typically low in the MHD inertial range, increases significantly when crossing
ion scales and its value in the sub-ion range is a function of the total plasma
beta only, as expected from theoretical predictions, with higher magnetic
compressibility for higher beta. Moreover, we observe that this increase has a
gradual trend from low to high beta values in the in situ data; this behaviour
is well captured by the numerical simulations. The level of magnetic field
compressibility that is observed in situ and in the simulations is in fairly
good agreement with theoretical predictions, especially at high beta,
suggesting that in the kinetic range explored the turbulence is supported by
low-frequency and highly-oblique fluctuations in pressure balance, like kinetic
Alfv\'en waves or other slowly evolving coherent structures.Comment: Manuscript submitted to Frontiers Astronomy and Space Sciences,
Research Topic: Improving the Understanding of Kinetic Processes in Solar
Wind and Magnetosphere: From CLUSTER to MM
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