10,084 research outputs found
Magneto-acoustic waves in sunspots from observations and numerical simulations
We study the propagation of waves from the photosphere to the chromosphere of
sunspots. From time series of cospatial Ca II H (including its line blends)
intensity spectra and polarimetric spectra of Si I 1082.7 nm and He I 1083.0 nm
we retrieve the line-of-sight velocity at several heights. The analysis of the
phase difference and amplification spectra shows standing waves for frequencies
below 4 mHz and propagating waves for higher frequencies, and allows us to
infer the temperature and height where the lines are formed. Using these
observational data, we have constructed a model of sunspot, and we have
introduced the velocity measured with the photospheric Si I 1082.7 nm line as a
driver. The numerically propagated wave pattern fits reasonably well with the
observed using the lines formed at higher layers, and the simulations reproduce
many of the observed features. The observed waves are slow MHD waves
propagating longitudinally along field lines.Comment: proceedings of GONG 2010/SOHO 24 meeting, June 27 - July 2, 2010,
Aix-en-Provence, Franc
Value sets of sparse polynomials
We obtain a new lower bound on the size of value set f(F_p) of a sparse
polynomial f in F_p[X] over a finite field of p elements when p is prime. This
bound is uniform with respect of the degree and depends on some natural
arithmetic properties of the degrees of the monomial terms of f and the number
of these terms. Our result is stronger than those which canted be extracted
from the bounds on multiplicities of individual values in f(F_p)
Spiral-shaped wavefronts in a sunspot umbra
Solar active regions show a wide variety of oscillatory phenomena. The
presence of the magnetic field leads to the appearance of several wave modes,
whose behavior is determined by the sunspot thermal and magnetic structure. We
aim to study the relation between the umbral and penumbral waves observed at
the high photosphere and the magnetic field topology of the sunspot.
Observations of the sunspot in active region NOAA 12662 obtained with the
GREGOR telescope (Observatorio del Teide, Spain) were acquired on 2017 June 17.
The data set includes a temporal series in the Fe I 5435 \AA\ line obtained
with the imaging spectrograph GREGOR Fabry-P\'erot Interferometer (GFPI) and a
spectropolarimetric raster map acquired with the GREGOR Infrared Spectrograph
(GRIS) in the 10830 \AA\ spectral region. The Doppler velocity deduced from the
restored Fe I 5435 \AA\ line has been determined, and the magnetic field vector
of the sunspot has been inferred from spectropolarimetric inversions of the Ca
I 10839 \AA\ and the Si I 10827 \AA\ lines. A two-armed spiral wavefront has
been identified in the evolution of the two-dimensional velocity maps from the
Fe I 5435 \AA\ line. The wavefronts initially move counterclockwise in the
interior of the umbra, and develop into radially outward propagating running
penumbral waves when they reach the umbra-penumbra boundary. The horizontal
propagation of the wavefronts approximately follows the direction of the
magnetic field, which shows changes in the magnetic twist with height and
horizontal position. The spiral wavefronts are interpreted as the visual
pattern of slow magnetoacoustic waves which propagate upward along magnetic
field lines. Their apparent horizontal propagation is due to their sequential
arrival to different horizontal positions at the formation height of the Fe I
5435 \AA\ line, as given by the inclination and orientation of the magnetic
field.Comment: Accepted for publication in A&
Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots
We study a recent result of Bourgain, Clozel and Kahane, a version of which
states that a sufficiently nice function
that coincides with its Fourier transform and vanishes at the origin has a root
in the interval , where the optimal satisfies . A similar result holds in higher dimensions. We improve the
one-dimensional result to , and the lower bound in
higher dimensions. We also prove that extremizers exist, and have infinitely
many double roots. With this purpose in mind, we establish a new structure
statement about Hermite polynomials which relates their pointwise evaluation to
linear flows on the torus, and applies to other families of orthogonal
polynomials as well.Comment: 26 pages, 4 figure
Multiplicative Order of Gauss Periods
We obtain a lower bound on the multiplicative order of Gauss periods which
generate normal bases over finite fields. This bound improves the previous
bound of J. von zur Gathen and I. E. Shparlinski.Comment: 9 page
Is the Theta+ a K pi N bound state?
Following a recent suggestion that the could be a bound
state we perform an investigation under the light of the meson meson and meson
baryon dynamics provided by the chiral Lagrangians and using methods currently
employed to dynamically generate meson and baryon resonances by means of
unitary extensions of chiral perturbation theory. We consider two body and
three body forces and examine the possibility of a bound state below the three
particle pion-kaon-nucleon and above the kaon-nucleon thresholds. Although we
find indeed an attractive interaction in the case of isospin I=0 and
spin-parity , the interaction is too weak to bind the system. If we
arbitrarily add to the physically motivated potential the needed strength to
bind the system and with such strong attraction evaluate the decay width into
, this turns out to be small. A discussion on further work in this
direction is done.Comment: Change of title and few sentences, size of two graphs. References
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Nonlinear Cointegration and Nonlinear Error Correction: Record Counting Cointegration Tests
In this article we propose a record counting cointegration (RCC) test that is robust to nonlinearities and certain types of structural breaks. The RCC test is based on the synchronicity property of the jumps (new records) of cointegrated series, counting the number of jumps that simultaneously occur in both series. We obtain the rate of convergence of the RCC statistics under the null and alternative hypothesis. Since the asymptotic distribution of RCC under the null hypothesis of a unit root depends on the short-run dependence of the cointegrated series, we propose a small sample correction and show by Monte Carlo simulation techniques their excellent small sample behaviour. Finally, we apply our new cointegration test statistic to several financial and macroeconomic time series that have certain structural breaks and nonlinearities.Publicad
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