114,208 research outputs found
Chirality, extended MHD statistics and solar wind turbulence
We unite the one-flow-dominated-state (OFDS) argument of
\citet{MeyrandGaltierPRL12} with the one-chiral-sector-dominated-state (OCSCS)
one \citep[][]{hydrochirality} to form a nonlinear
extended-magnetohydrodynamics (XMHD) theory for the solar wind turbulence
(SWT), \textbf{ranging from the MHD- to subproton-, and even to
subelectron-scale regimes} \citep[modifying the theory
of][]{AbdelhamidLingamMahajanAPJ16}. Degenerate chiral states in
\citet{MiloshevichLingamMorrisonNJP17}'s XMHD absolute equilibria are exposed
with helical representation, to offer the basis of replacing the linear wave
(of infinitesimal or arbitrarily finite amplitudes) arguments of previous
theories with OCSDS. Possible connection of the OFDS-plus-OCSDS theory with the
local minimal-energy/stability principle is also discussed.Comment: uncorrected versio
Statistical mechanics of -dimensional flows and cylindrically reduced passive scalars
Statistical properties of -dimensional incompressible flows with and
without cylindrical reduction are studied, leading to several explanations and
conjectures about turbulent flows and passive scalars, such as the
de-correlation between the flow and scalar, reduction of passive scalar
intermittency in the bottleneck regime, et al. The absolute-equilibrium
analyses assure the correctness of a recent numerical result. It is implied
that passive scalar(s) in two-dimensional (2D) space can be fundamentally
different to those in , concerning the correlations with the flow, which
is not considered in the celebrated Kraichnan model. The possibility of genuine
inverse transfer to large scales of 2D passive scalar energy, together with the
advection energy, is indicated. The compressible situation is also briefly
remarked in the end, in particular the absence of density in a nontrivial
Casimir which, without boundary contribution, also vanishes for .Comment: three figures added for better illustratio
Fast rotating flows in high spatial dimensions
The central result about fast rotating-flow structures is the Taylor-Proudman
theorem (TPT) which connects various aspects of the dynamics. Taylor's
geometrical proof of TPT is reproduced and extended substantially, with Lie's
theory for general frozen-in laws and the consequent generalized invariant
circulation theorems, to compressible flows and to -dimensional Euclidean
space () with . The TPT relatives, the reduced models
(with particular interests on passive-scalar problems), the inertial (resonant)
waves and the higher-order corrections, are discussed coherently for a
comprehensive bird view of rotating flows in high spatial dimensions.Comment: plasmas are neutralized, for the time being, and the bibliography is
greatly enriched with in particular many more relevant references of
mathematical analyse
Isotropic polarization of compressible flows
The helical absolute equilibrium of a compressible adiabatic flow presents
not only the polarization between the two purely helical modes of opposite
chiralities but also that between the vortical and acoustic modes, deviating
from the equipartition predicted by {\sc Kraichnan, R. H.} [1955 The Journal of
the Acoustical Society of America {\bf 27}, 438--441.]. Due to the existence of
the acoustic mode, even if all Fourier modes of one chiral sector in the
sharpened Helmholtz decomposition [{\sc Moses, H. E.} 1971 SIAM ~(Soc. Ind.
Appl. Math.) J. Appl. Math. {\bf 21}, 114--130] are thoroughly truncated,
leaving the system with positive definite helicity and energy, negative
temperature and the corresponding large-scale concentration of vortical modes
are not allowed, unlike the incompressible case.Comment: an Erratum or Clarification is added to a remark on Page
Note on specific chiral ensembles of statistical hydrodynamics: "order function" for transition of turbulence transfer scenarios
Hydrodynamic helicity signatures the parity symmetry breaking, chirality, of
the flow. Statistical hydrodynamics thus respect chirality, as symmetry
breaking and restoration are key to their fundamentals, such as the spectral
transfer direction and its mechanism. Homochiral sub-system of
three-dimensional (3D) Navier-Stokes isotropic turbulence has been numerically
realized with helical representation technique to present inverse energy
cascade [Biferale et al., Phys. Rev. Lett., {\bf 108}, 164501 (2012)]. The
situation is analogous to 2D turbulence where inverse energy cascade, or more
generally energy-enstrophy dual cascade scenario, was argued with the help of a
negative temperature state of the absolute equilibrium by Kraichnan. Indeed, if
the helicity in such a system is taken to be positive without loss of
generality, a corresponding negative temperature state can be identified [Zhu
et al., J. Fluid Mech., {\bf 739}, 479 (2014)]. Here, for some specific chiral
ensembles of turbulence, we show with the corresponding absolute equilibria
that even if the helicity distribution over wavenumbers is sign definite,
different \textit{ansatzes} of the shape function, defined by the ratio between
the specific helicity and energy spectra , imply distinct
transfer directions, and we could have inverse-helicity and forward-energy dual
transfers (with, say, resulting in absolute equilibrium
modal spectral density of energy , exactly
the enstrophy one of two-dimensional Euler by Kraichan), simultaneous forward
transfers (with ), or even no simply-directed transfer (with,
say, non-monotonic ), besides the inverse-energy and
forward-helicity dual transfers (with, say, as in the homochiral
case)
Equilibrium and non-equilibrium time-reversible dynamical ensembles relevant to chiral turbulence
Ideas and theories of turbulence based on modifying the Navier-Stokes
equation, to obtain equilibrium and non-equilibrium time-reversible dynamical
ensembles relevant to helical turbulence, are presented. Discussions of
controlling helicity to control the aerodynamic force, heat and noise are
presented, together with the compressible turbulence relevant statistical
mechanics analysis. A helical time-reversible system for nonequilibrium
dynamical ensemble is constructed. Applications are also remarked.Comment: main text in Chinese with English tittle and abstrac
Comment on "Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence"
We argue that the constraints on transfers, given in the Letter [G. Plunk and
T. Tatsuno, Phys. Rev. Lett. {\bf 106}, 165003 (2011)], but not correctly, do
not give the transfer and/or cascade directions which however can be assisted
by the absolute equilibria calculated in this Comment, following Kraichnan [R.
H. Kraichnan, Phys. Fluids {\bf 102}, 1417 (1967)]. One of the important
statements about the transfers with only one or no diagonal component can be
shown to be inappropriate according to the fundamental dynamics. Some
mathematical mistakes are pointed out.Comment: the typos in some formulae corrected; some rewording (say,
acknowledging the Letter's contributions in the beginning of the Comment)
mad
On the exact solutions of (magneto)hydrodynamic systems and the superposition principles of nonlinear helical waves
The principles of restricted superposition of circularly polarized
arbitrary-amplitude waves for several hydrodynamic type models are illustrated
systematically with helical representation in a unified sense. It is shown that
the only general modes satisfying arbitrary-amplitude superposition to kill the
generic nonlinearity are the mono-wavelength homochiral Beltrami mode and the
one-dimensional-two-component stratified vorticity mode, which we call the XYz
flow/wave; while, there are other special superposition principles for some
specific cases. We try to remark on the possible connections with the geo-
and/or astro-physical fluid and magnetohydrodynamic turbulence issues, such as
the rotating turbulence, dynamo and solar atmosphere turbulence, especially
with the introduction of disorder locally frozen in some (randomly distributed)
space-time regions. Recent disagreements about exact solutions of Hall and
fully two-fluid magnetohydrodynamics are also settled down by such a treatment.
This work complements, by studying the modes which completely kill the triadic
interactions or the nonlinearities, previous studies on the thermalization
purely from the triadic interactions, and in turn offers alternative
perspectives of the nonlinearities
Group Variable Selection via a Hierarchical Lasso and Its Oracle Property
In many engineering and scientific applications, prediction variables are
grouped, for example, in biological applications where assayed genes or
proteins can be grouped by biological roles or biological pathways. Common
statistical analysis methods such as ANOVA, factor analysis, and functional
modeling with basis sets also exhibit natural variable groupings. Existing
successful group variable selection methods such as Antoniadis and Fan (2001),
Yuan and Lin (2006) and Zhao, Rocha and Yu (2009) have the limitation of
selecting variables in an "all-in-all-out" fashion, i.e., when one variable in
a group is selected, all other variables in the same group are also selected.
In many real problems, however, we may want to keep the flexibility of
selecting variables within a group, such as in gene-set selection. In this
paper, we develop a new group variable selection method that not only removes
unimportant groups effectively, but also keeps the flexibility of selecting
variables within a group. We also show that the new method offers the potential
for achieving the theoretical "oracle" property as in Fan and Li (2001) and Fan
and Peng (2004).Comment: 43 pages, 2 figure
Taming heavy-tailed features by shrinkage
In this work, we focus on a variant of the generalized linear model (GLM)
called corrupted GLM (CGLM) with heavy-tailed features and responses. To
robustify the statistical inference on this model, we propose to apply
-norm shrinkage to the feature vectors in the low-dimensional regime
and apply elementwise shrinkage to them in the high-dimensional regime. Under
bounded fourth moment assumptions, we show that the maximum likelihood
estimator (MLE) based on the shrunk data enjoys nearly the minimax optimal rate
with an exponential deviation bound. Our simulations demonstrate that the
proposed feature shrinkage significantly enhances the statistical performance
in linear regression and logistic regression on heavy-tailed data. Finally, we
apply our shrinkage principle to guard against mislabeling and image noise in
the human-written digit recognition problem. We add an -norm shrinkage
layer to the original neural net and reduce the testing misclassification rate
by more than relatively in the presence of mislabeling and image noise.Comment: 24 page
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