6,946 research outputs found
Whistler Wave Turbulence in Solar Wind Plasma
Whistler waves are present in solar wind plasma. These waves possess
characteristic turbulent fluctuations that are characterized typically by the
frequency and length scales that are respectively bigger than ion gyro
frequency and smaller than ion gyro radius. The electron inertial length is an
intrinsic length scale in whistler wave turbulence that distinguishably divides
the high frequency solar wind turbulent spectra into scales smaller and bigger
than the electron inertial length. We present nonlinear three dimensional, time
dependent, fluid simulations of whistler wave turbulence to investigate their
role in solar wind plasma. Our simulations find that the dispersive whistler
modes evolve entirely differently in the two regimes. While the dispersive
whistler wave effects are stronger in the large scale regime, they do not
influence the spectral cascades which are describable by a Kolmogorov-like
spectrum. By contrast, the small scale turbulent fluctuations
exhibit a Navier-Stokes like evolution where characteristic turbulent eddies
exhibit a typical hydrodynamic turbulent spectrum. By virtue of
equipartition between the wave velocity and magnetic fields, we quantify the
role of whistler waves in the solar wind plasma fluctuations.Comment: To appear in the Proceedings of Solar Wind 1
Self-consistent Simulations of Plasma-Neutral in a Partially Ionized Astrophysical Turbulent Plasma
A local turbulence model is developed to study energy cascades in the
heliosheath and outer heliosphere (OH) based on self-consistent two-dimensional
fluid simulations. The model describes a partially ionized magnetofluid OH that
couples a neutral hydrogen fluid with a plasma primarily through
charge-exchange interactions. Charge-exchange interactions are ubiquitous in
warm heliospheric plasma, and the strength of the interaction depends largely
on the relative speed between the plasma and the neutral fluid. Unlike
small-length scale linear collisional dissipation in a single fluid,
charge-exchange processes introduce channels that can be effective on a variety
of length scales that depend on the neutral and plasma densities, temperature,
relative velocities, charge-exchange cross section, and the characteristic
length scales. We find, from scaling arguments and nonlinear coupled fluid
simulations, that charge-exchange interactions modify spectral transfer
associated with large-scale energy-containing eddies. Consequently, the
turbulent cascade rate prolongs spectral transfer among inertial range
turbulent modes. Turbulent spectra associated with the neutral and plasma
fluids are therefore steeper than those predicted by Kolmogorov's
phenomenology. Our work is important in the context of the global heliospheric
interaction, the energization and transport of cosmic rays, gamma-ray bursts,
interstellar density spectra, etc. Furthermore, the plasma-neutral coupling is
crucial in understanding the energy dissipation mechanism in molecular clouds
and star formation processes.Comment: To appear in the Proceedings of Solar Wind 1
On stepdown control of the false discovery proportion
Consider the problem of testing multiple null hypotheses. A classical
approach to dealing with the multiplicity problem is to restrict attention to
procedures that control the familywise error rate (), the probability of
even one false rejection. However, if is large, control of the is so
stringent that the ability of a procedure which controls the to detect
false null hypotheses is limited. Consequently, it is desirable to consider
other measures of error control. We will consider methods based on control of
the false discovery proportion () defined by the number of false
rejections divided by the total number of rejections (defined to be 0 if there
are no rejections). The false discovery rate proposed by Benjamini and Hochberg
(1995) controls . Here, we construct methods such that, for any
and , . Based on -values of
individual tests, we consider stepdown procedures that control the ,
without imposing dependence assumptions on the joint distribution of the
-values. A greatly improved version of a method given in Lehmann and Romano
\citer10 is derived and generalized to provide a means by which any sequence of
nondecreasing constants can be rescaled to ensure control of the . We also
provide a stepdown procedure that controls the under a dependence
assumption.Comment: Published at http://dx.doi.org/10.1214/074921706000000383 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stepup procedures for control of generalizations of the familywise error rate
Consider the multiple testing problem of testing null hypotheses
. A classical approach to dealing with the multiplicity problem is
to restrict attention to procedures that control the familywise error rate
(), the probability of even one false rejection. But if is
large, control of the is so stringent that the ability of a
procedure that controls the to detect false null hypotheses is
limited. It is therefore desirable to consider other measures of error control.
This article considers two generalizations of the . The first is
the , in which one is willing to tolerate or more false
rejections for some fixed . The second is based on the false discovery
proportion (), defined to be the number of false rejections
divided by the total number of rejections (and defined to be 0 if there are no
rejections). Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995)
289--300] proposed control of the false discovery rate (), by
which they meant that, for fixed , . Here,
we consider control of the in the sense that, for fixed
and , . Beginning with any
nondecreasing sequence of constants and -values for the individual tests, we
derive stepup procedures that control each of these two measures of error
control without imposing any assumptions on the dependence structure of the
-values. We use our results to point out a few interesting connections with
some closely related stepdown procedures. We then compare and contrast two
-controlling procedures obtained using our results with the
stepup procedure for control of the of Benjamini and Yekutieli
[Ann. Statist. 29 (2001) 1165--1188].Comment: Published at http://dx.doi.org/10.1214/009053606000000461 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the uniform asymptotic validity of subsampling and the bootstrap
This paper provides conditions under which subsampling and the bootstrap can
be used to construct estimators of the quantiles of the distribution of a root
that behave well uniformly over a large class of distributions .
These results are then applied (i) to construct confidence regions that behave
well uniformly over in the sense that the coverage probability
tends to at least the nominal level uniformly over and (ii) to
construct tests that behave well uniformly over in the sense that
the size tends to no greater than the nominal level uniformly over
. Without these stronger notions of convergence, the asymptotic
approximations to the coverage probability or size may be poor, even in very
large samples. Specific applications include the multivariate mean, testing
moment inequalities, multiple testing, the empirical process and U-statistics.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1051 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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