4,957 research outputs found
Fractal Measures and Nonlinear Dynamics of Overcontact Binaries
Overcontact binary stars are systems of two stars where the component stars
are in contact with each other. This implies that they share a common envelope
of gas. In this work we seek signatures of nonlinearity and chaos in these
stars by using time series analysis techniques. We use three main techniques,
namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The
former two are calculated from the reconstructed dynamics, while the latter is
calculated from the Fourier transforms of the time series of intensity
variations(light curves) of these stars. Our dataset consists of data from 463
overcontact binary stars in the Kepler field of view [1]. Our analysis
indicates nonlinearity and signatures of chaos in almost all the light curves.
We also explore whether the underlying nonlinear properties of the stars are
related to their physical properties like fill-out-factor, a measure of the
extend of contact between the components of an overcontact binary system . We
observe that significant correlations exist between the fill out factor and the
nonlinear quantifiers. This correlation is more pronounced in specific
subcategories constructed based on the mass ratios and effective temperatures
of the binaries. The correlations observed can be indicative of variations in
the nonlinear properties of the star as it ages. We believe that this study
relating nonlinear and astrophysical properties of binary stars is the first of
its kind and is an important starting point for such studies in other
astrophysical objects displaying nonlinear dynamical behaviour.Comment: 17 pages, 12 figures, submitted to Communications in Nonlinear
Science and Numerical Simulatio
Revised research about chaotic dynamics in Manko et al. spacetime
A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that
chaos phenomenon of test particles in gravitational field of rotating neutron
stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.)
metric can only occur when the stars have oblate deformation. But the chaotic
motions they found are limited in a very narrow zone which is very close to the
center of the massive bodies. This paper argues that this is impossible because
the region is actually inside of the stars, so the motions cannot exist at this
place. In this paper, we scan all parameters space and find chaos and unstable
fixed points outside of stars with big mass-quadrupole moments. The
calculations show that chaos can only occur when the stars have prolate
deformation. Because real deformation of stars should be oblate, all orbits of
test particles around the rotating neutron stars described by Manko et al.
solutions are regular. The case of nonzero dipolar magnetic moment has also
been taken into account in this study.Comment: 6 pages, 5 figure
The chaotic solar cycle II. Analysis of cosmogenic 10Be data
Context. The variations of solar activity over long time intervals using a
solar activity reconstruction based on the cosmogenic radionuclide 10Be
measured in polar ice cores are studied. Methods. By applying methods of
nonlinear dynamics, the solar activity cycle is studied using solar activity
proxies that have been reaching into the past for over 9300 years. The
complexity of the system is expressed by several parameters of nonlinear
dynamics, such as embedding dimension or false nearest neighbors, and the
method of delay coordinates is applied to the time series. We also fit a damped
random walk model, which accurately describes the variability of quasars, to
the solar 10Be data and investigate the corresponding power spectral
distribution. The periods in the data series were searched by the Fourier and
wavelet analyses. The solar activity on the long-term scale is found to be on
the edge of chaotic behavior. This can explain the observed intermittent period
of longer lasting solar activity minima. Filtering the data by eliminating
variations below a certain period (the periods of 380 yr and 57 yr were used)
yields a far more regular behavior of solar activity. A comparison between the
results for the 10Be data with the 14C data shows many similarities. Both
cosmogenic isotopes are strongly correlated mutually and with solar activity.
Finally, we find that a series of damped random walk models provides a good fit
to the 10Be data with a fixed characteristic time scale of 1000 years, which is
roughly consistent with the quasi-periods found by the Fourier and wavelet
analyses.Comment: 8 pages, 11 figure
Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data
The knowledge of transitions between regular, laminar or chaotic behavior is
essential to understand the underlying mechanisms behind complex systems. While
several linear approaches are often insufficient to describe such processes,
there are several nonlinear methods which however require rather long time
observations. To overcome these difficulties, we propose measures of complexity
based on vertical structures in recurrence plots and apply them to the logistic
map as well as to heart rate variability data. For the logistic map these
measures enable us not only to detect transitions between chaotic and periodic
states, but also to identify laminar states, i.e. chaos-chaos transitions. The
traditional recurrence quantification analysis fails to detect the latter
transitions. Applying our new measures to the heart rate variability data, we
are able to detect and quantify the laminar phases before a life-threatening
cardiac arrhythmia occurs thereby facilitating a prediction of such an event.
Our findings could be of importance for the therapy of malignant cardiac
arrhythmias
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