31,372 research outputs found
Standing sausage modes in coronal loops with plasma flow
Magnetohydrodynamic waves are important for diagnosing the physical
parameters of coronal plasmas. Field-aligned flows appear frequently in coronal
loops.We examine the effects of transverse density and plasma flow structuring
on standing sausage modes trapped in coronal loops, and examine their
observational implications. We model coronal loops as straight cold cylinders
with plasma flow embedded in a static corona. An eigen-value problem governing
propagating sausage waves is formulated, its solutions used to construct
standing modes. Two transverse profiles are distinguished, one being the
generalized Epstein distribution (profile E) and the other (N) proposed
recently in Nakariakov et al.(2012). A parameter study is performed on the
dependence of the maximum period and cutoff length-to-radius
ratio in the trapped regime on the density parameters
( and profile steepness ) and flow parameters (magnitude
and profile steepness ). For either profile, introducing a flow
reduces relative to the static case. depends
sensitively on for profile N but is insensitive to for profile E. By
far the most important effect a flow introduces is to reduce the capability for
loops to trap standing sausage modes: may be
substantially reduced in the case with flow relative to the static one. If the
density distribution can be described by profile N, then measuring the sausage
mode period can help deduce the density profile steepness. However, this
practice is not feasible if profile E better describes the density
distribution. Furthermore, even field-aligned flows with magnitudes
substantially smaller than the ambient Alfv\'en speed can make coronal loops
considerably less likely to support trapped standing sausage modes.Comment: 11 pages, 9 figures, to appear in Astronomy & Astrophysic
Spatial damping of propagating sausage waves in coronal cylinders
Sausage modes are important in coronal seismology. Spatially damped
propagating sausage waves were recently observed in the solar atmosphere. We
examine how wave leakage influences the spatial damping of sausage waves
propagating along coronal structures modeled by a cylindrical density
enhancement embedded in a uniform magnetic field. Working in the framework of
cold magnetohydrodynamics, we solve the dispersion relation (DR) governing
sausage waves for complex-valued longitudinal wavenumber at given real
angular frequencies . For validation purposes, we also provide
analytical approximations to the DR in the low-frequency limit and in the
vicinity of , the critical angular frequency separating trapped
from leaky waves. In contrast to the standing case, propagating sausage waves
are allowed for much lower than . However, while able
to direct their energy upwards, these low-frequency waves are subject to
substantial spatial attenuation. The spatial damping length shows little
dependence on the density contrast between the cylinder and its surroundings,
and depends only weakly on frequency. This spatial damping length is of the
order of the cylinder radius for , where
and are the cylinder radius and the Alfv\'en speed in the
cylinder, respectively. We conclude that if a coronal cylinder is perturbed by
symmetric boundary drivers (e.g., granular motions) with a broadband spectrum,
wave leakage efficiently filters out the low-frequency components.Comment: 6 pages, 2 figures, to appear in Astronomy & Astrophysic
Information Cascades on Arbitrary Topologies
In this paper, we study information cascades on graphs. In this setting, each
node in the graph represents a person. One after another, each person has to
take a decision based on a private signal as well as the decisions made by
earlier neighboring nodes. Such information cascades commonly occur in practice
and have been studied in complete graphs where everyone can overhear the
decisions of every other player. It is known that information cascades can be
fragile and based on very little information, and that they have a high
likelihood of being wrong.
Generalizing the problem to arbitrary graphs reveals interesting insights. In
particular, we show that in a random graph , for the right value of
, the number of nodes making a wrong decision is logarithmic in . That
is, in the limit for large , the fraction of players that make a wrong
decision tends to zero. This is intriguing because it contrasts to the two
natural corner cases: empty graph (everyone decides independently based on his
private signal) and complete graph (all decisions are heard by all nodes). In
both of these cases a constant fraction of nodes make a wrong decision in
expectation. Thus, our result shows that while both too little and too much
information sharing causes nodes to take wrong decisions, for exactly the right
amount of information sharing, asymptotically everyone can be right. We further
show that this result in random graphs is asymptotically optimal for any
topology, even if nodes follow a globally optimal algorithmic strategy. Based
on the analysis of random graphs, we explore how topology impacts global
performance and construct an optimal deterministic topology among layer graphs
Primordial Gravitational Waves Measurements and Anisotropies of CMB Polarization Rotation
Searching for the signal of primordial gravitational waves in the B-modes
(BB) power spectrum is one of the key scientific aims of the cosmic microwave
background (CMB) polarization experiments. However, this could be easily
contaminated by several foreground issues, such as the thermal dust emission.
In this paper we study another mechanism, the cosmic birefringence, which can
be introduced by a CPT-violating interaction between CMB photons and an
external scalar field. Such kind of interaction could give rise to the rotation
of the linear polarization state of CMB photons, and consequently induce the
CMB BB power spectrum, which could mimic the signal of primordial gravitational
waves at large scales. With the recent polarization data of BICEP2 and the
joint analysis data of BICEP2/Keck Array and Planck, we perform a global
fitting analysis on constraining the tensor-to-scalar ratio by considering
the polarization rotation angle which can be separated into a background
isotropic part and a small anisotropic part. Since the data of BICEP2 and Keck
Array experiments have already been corrected by using the "self-calibration"
method, here we mainly focus on the effects from the anisotropies of CMB
polarization rotation angle. We find that including the anisotropies in the
analysis could slightly weaken the constraints on , when using current CMB
polarization measurements. We also simulate the mock CMB data with the
BICEP3-like sensitivity. Very interestingly, we find that if the effects of the
anisotropic polarization rotation angle can not be taken into account properly
in the analysis, the constraints on will be dramatically biased. This
implies that we need to break the degeneracy between the anisotropies of the
CMB polarization rotation angle and the CMB primordial tensor perturbations, in
order to measure the signal of primordial gravitational waves accurately.Comment: 7 pages, 5 figure
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