5,398 research outputs found
Structures in a class of magnetized scale-free discs
We construct analytically stationary global configurations for both aligned
and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an
axisymmetric background MHD disc with a power-law surface mass density
, a coplanar azimuthal magnetic field , a consistent self-gravity and a power-law rotation curve
where is the linear azimuthal gas rotation speed.
The barotropic equation of state is adopted for both MHD
background equilibrium and coplanar MHD perturbations where is the
vertically integrated pressure and is the barotropic index. For a
scale-free background MHD equilibrium, a relation exists among ,
, and such that only one parameter (e.g., ) is
independent. For a linear axisymmetric stability analysis, we provide global
criteria in various parameter regimes. For nonaxisymmetric aligned and
logarithmic spiral cases, two branches of perturbation modes (i.e., fast and
slow MHD density waves) can be derived once is specified. To complement
the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the
analysis to a wider range of . As an example of illustration,
we discuss specifically the case when the background magnetic field
is force-free. Angular momentum conservation for coplanar MHD perturbations and
other relevant aspects of our approach are discussed.Comment: 25 page
Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs
We construct aligned and unaligned stationary perturbation configurations in
a composite system of stellar and coplanarly magnetized gaseous singular
isothermal discs (SIDs) coupled by gravity. In comparison with SID problems
studied earlier, there exist three possible classes of stationary solutions
allowed by more dynamic freedoms. Our exact global perturbation solutions and
critical points are valuable for testing numerical magnetohydrodynamic codes.
For galactic applications, our model analysis contains more realistic elements
and offer useful insights for structures and dynamics of disc galaxies
consisting of stars and magnetized gas.Comment: 25 pages, 31 figures, accepted by Monthly Notices of Royal
Astronomical Society, style files include
Periodicities in Solar Coronal Mass Ejections
Mid-term quasi-periodicities in solar coronal mass ejections (CMEs) during
the most recent solar maximum cycle 23 are reported here for the first time
using the four-year data (February 5, 1999 to February 10, 2003) of the Large
Angle Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric
Observatory (SOHO). In parallel, mid-term quasi-periodicities in solar X-ray
flares (class >M5.0) from the Geosynchronous Operational Environment Satellites
(GOES) and in daily averages of Ap index for geomagnetic disturbances from the
World Data Center (WDC) at the International Association for Geomagnetism and
Aeronomy (IAGA) are also examined for the same four-year time span. Several
conceptual aspects of possible equatorially trapped Rossby-type waves at and
beneath the solar photosphere are discussed.Comment: Accepted by MNRAS, 6 figure
Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc
Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density N which travels at a relevant radial group speed Cg. The wave energy surface density ℰ and the wave angular momentum surface density J are related to N by ℰ=ωN and J=mN respectively, where ω is the angular frequency in an inertial frame of reference and the integer m, proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discusse
Communication-Efficient Distributed Estimation and Inference for Cox's Model
Motivated by multi-center biomedical studies that cannot share individual
data due to privacy and ownership concerns, we develop communication-efficient
iterative distributed algorithms for estimation and inference in the
high-dimensional sparse Cox proportional hazards model. We demonstrate that our
estimator, even with a relatively small number of iterations, achieves the same
convergence rate as the ideal full-sample estimator under very mild conditions.
To construct confidence intervals for linear combinations of high-dimensional
hazard regression coefficients, we introduce a novel debiased method, establish
central limit theorems, and provide consistent variance estimators that yield
asymptotically valid distributed confidence intervals. In addition, we provide
valid and powerful distributed hypothesis tests for any coordinate element
based on a decorrelated score test. We allow time-dependent covariates as well
as censored survival times. Extensive numerical experiments on both simulated
and real data lend further support to our theory and demonstrate that our
communication-efficient distributed estimators, confidence intervals, and
hypothesis tests improve upon alternative methods
Robust High-dimensional Tuning Free Multiple Testing
A stylized feature of high-dimensional data is that many variables have heavy
tails, and robust statistical inference is critical for valid large-scale
statistical inference. Yet, the existing developments such as Winsorization,
Huberization and median of means require the bounded second moments and involve
variable-dependent tuning parameters, which hamper their fidelity in
applications to large-scale problems. To liberate these constraints, this paper
revisits the celebrated Hodges-Lehmann (HL) estimator for estimating location
parameters in both the one- and two-sample problems, from a non-asymptotic
perspective. Our study develops Berry-Esseen inequality and Cram\'{e}r type
moderate deviation for the HL estimator based on newly developed non-asymptotic
Bahadur representation, and builds data-driven confidence intervals via a
weighted bootstrap approach. These results allow us to extend the HL estimator
to large-scale studies and propose \emph{tuning-free} and \emph{moment-free}
high-dimensional inference procedures for testing global null and for
large-scale multiple testing with false discovery proportion control. It is
convincingly shown that the resulting tuning-free and moment-free methods
control false discovery proportion at a prescribed level. The simulation
studies lend further support to our developed theory.Comment: In this paper, we develop tuning-free and moment-free high
dimensional inference procedures
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