4,640 research outputs found
Data granulation by the principles of uncertainty
Researches in granular modeling produced a variety of mathematical models,
such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets,
which are all suitable to characterize the so-called information granules.
Modeling of the input data uncertainty is recognized as a crucial aspect in
information granulation. Moreover, the uncertainty is a well-studied concept in
many mathematical settings, such as those of probability theory, fuzzy set
theory, and possibility theory. This fact suggests that an appropriate
quantification of the uncertainty expressed by the information granule model
could be used to define an invariant property, to be exploited in practical
situations of information granulation. In this perspective, a procedure of
information granulation is effective if the uncertainty conveyed by the
synthesized information granule is in a monotonically increasing relation with
the uncertainty of the input data. In this paper, we present a data granulation
framework that elaborates over the principles of uncertainty introduced by
Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is
possible to apply such principles regardless of the input data type and the
specific mathematical setting adopted for the information granules. The
proposed framework is conceived (i) to offer a guideline for the synthesis of
information granules and (ii) to build a groundwork to compare and
quantitatively judge over different data granulation procedures. To provide a
suitable case study, we introduce a new data granulation technique based on the
minimum sum of distances, which is designed to generate type-2 fuzzy sets. We
analyze the procedure by performing different experiments on two distinct data
types: feature vectors and labeled graphs. Results show that the uncertainty of
the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference
Hydrodynamical simulations of convection-related stellar micro-variability. II. The enigmatic granulation background of the COROT target HD49933
Local-box hydrodynamical model atmospheres provide statistical information
about a star's emergent radiation field which allows one to predict the level
of its granulation-related micro-variability. Space-based photometry is now
sufficiently accurate to test model predictions. We aim to model the
photometric granulation background of HD49933 as well as the Sun, and compare
the predictions to the measurements obtained by the COROT and SOHO satellite
missions. We construct hydrodynamical model atmospheres representing HD49933
and the Sun, and use a previously developed scaling technique to obtain the
observable disk-integrated brightness fluctuations. We further performed
exploratory magneto-hydrodynamical simulations to gauge the impact of small
scale magnetic fields on the synthetic light-curves. We find that the
granulation-related brightness fluctuations depend on metallicity. We obtain a
satisfactory correspondence between prediction and observation for the Sun,
validating our approach. For HD49933, we arrive at a significant
over-estimation by a factor of two to three in total power. Locally generated
magnetic fields are unlikely to be responsible, otherwise existing fields would
need to be rather strong to sufficiently suppress the granulation signal.
Presently suggested updates on the fundamental stellar parameters do not
improve the correspondence; however, an ad-hoc increase of the HD49933 surface
gravity by about 0.2dex would eliminate most of the discrepancy. We diagnose a
puzzling discrepancy between the predicted and observed granulation background
in HD49933, with only rather ad-hoc ideas for remedies at hand.Comment: 7 pages, 5 figures, accepted for publication in A&
Quiet-Sun imaging asymmetries in NaI D1 compared with other strong Fraunhofer lines
Imaging spectroscopy of the solar atmosphere using the NaI D1 line yields
marked asymmetry between the blue and red line wings: sampling a quiet-Sun area
in the blue wing displays reversed granulation, whereas sampling in the red
wing displays normal granulation. The MgI b2 line of comparable strength does
not show this asymmetry, nor does the stronger CaII 8542 line. We demonstrate
the phenomenon with near-simultaneous spectral images in NaI D1, MgI b2, and
CaII 8542 from the Swedish 1-m Solar Telescope. We then explain it with
line-formation insights from classical 1D modeling and with a 3D
magnetohydrodynamical simulation combined with NLTE spectral line synthesis
that permits detailed comparison with the observations in a common format. The
cause of the imaging asymmetry is the combination of correlations between
intensity and Dopplershift modulation in granular overshoot and the sensitivity
to these of the steep profile flanks of the NaI D1 line. The MgI b2 line has
similar core formation but much wider wings due to larger opacity buildup and
damping in the photosphere. Both lines obtain marked core asymmetry from
photospheric shocks in or near strong magnetic concentrations, less from
higher-up internetwork shocks that produce similar asymmetry in the spatially
averaged CaII 8542 profile.Comment: Accepted by Astron & Astrophys. In each in-text citation the year
links to the corresponding ADS abstract pag
Solar Magnetic Tracking. I. Software Comparison and Recommended Practices
Feature tracking and recognition are increasingly common tools for data
analysis, but are typically implemented on an ad-hoc basis by individual
research groups, limiting the usefulness of derived results when selection
effects and algorithmic differences are not controlled. Specific results that
are affected include the solar magnetic turnover time, the distributions of
sizes, strengths, and lifetimes of magnetic features, and the physics of both
small scale flux emergence and the small-scale dynamo. In this paper, we
present the results of a detailed comparison between four tracking codes
applied to a single set of data from SOHO/MDI, describe the interplay between
desired tracking behavior and parameterization of tracking algorithms, and make
recommendations for feature selection and tracking practice in future work.Comment: In press for Astrophys. J. 200
Measuring the Hidden Aspects of Solar Magnetism
2008 marks the 100th anniversary of the discovery of astrophysical magnetic
fields, when George Ellery Hale recorded the Zeeman splitting of spectral lines
in sunspots. With the introduction of Babcock's photoelectric magnetograph it
soon became clear that the Sun's magnetic field outside sunspots is extremely
structured. The field strengths that were measured were found to get larger
when the spatial resolution was improved. It was therefore necessary to come up
with methods to go beyond the spatial resolution limit and diagnose the
intrinsic magnetic-field properties without dependence on the quality of the
telescope used. The line-ratio technique that was developed in the early 1970s
revealed a picture where most flux that we see in magnetograms originates in
highly bundled, kG fields with a tiny volume filling factor. This led to
interpretations in terms of discrete, strong-field magnetic flux tubes embedded
in a rather field-free medium, and a whole industry of flux tube models at
increasing levels of sophistication. This magnetic-field paradigm has now been
shattered with the advent of high-precision imaging polarimeters that allow us
to apply the so-called "Second Solar Spectrum" to diagnose aspects of solar
magnetism that have been hidden to Zeeman diagnostics. It is found that the
bulk of the photospheric volume is seething with intermediately strong, tangled
fields. In the new paradigm the field behaves like a fractal with a high degree
of self-similarity, spanning about 8 orders of magnitude in scale size, down to
scales of order 10 m.Comment: To appear in "Magnetic Coupling between the Interior and the
Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and
Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200
Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere
Three-dimensional numerical simulations with CO5BOLD, a new radiation
hydrodynamics code, result in a dynamic, thermally bifurcated model of the
non-magnetic chromosphere of the quiet Sun. The 3-D model includes the middle
and low chromosphere, the photosphere, and the top of the convection zone,
where acoustic waves are excited by convective motions. While the waves
propagate upwards, they steepen into shocks, dissipate, and deposit their
mechanical energy as heat in the chromosphere. Our numerical simulations show
for the first time a complex 3-D structure of the chromospheric layers, formed
by the interaction of shock waves. Horizontal temperature cross-sections of the
model chromosphere exhibit a network of hot filaments and enclosed cool
regions. The horizontal pattern evolves on short time-scales of the order of
typically 20 - 25 seconds, and has spatial scales comparable to those of the
underlying granulation. The resulting thermal bifurcation, i.e., the
co-existence of cold and hot regions, provides temperatures high enough to
produce the observed chromospheric UV emission and -- at the same time --
temperatures cold enough to allow the formation of molecules (e.g., carbon
monoxide). Our 3-D model corroborates the finding by Carlsson & Stein (1994)
that the chromospheric temperature rise of semi-empirical models does not
necessarily imply an increase in the average gas temperature but can be
explained by the presence of substantial spatial and temporal temperature
inhomogeneities.Comment: 18 pages, 13 figures, accepted by Astronomy & Astrophysics (30/10/03
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