49,876 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
Effects of additive noise on the stability of glacial cycles
It is well acknowledged that the sequence of glacial-interglacial cycles is
paced by the astronomical forcing. However, how much is the sequence robust
against natural fluctuations associated, for example, with the chaotic motions
of atmosphere and oceans? In this article, the stability of the
glacial-interglacial cycles is investigated on the basis of simple conceptual
models. Specifically, we study the influence of additive white Gaussian noise
on the sequence of the glacial cycles generated by stochastic versions of
several low-order dynamical system models proposed in the literature. In the
original deterministic case, the models exhibit different types of attractors:
a quasiperiodic attractor, a piecewise continuous attractor, strange nonchaotic
attractors, and a chaotic attractor. We show that the combination of the
quasiperiodic astronomical forcing and additive fluctuations induce a form of
temporarily quantised instability. More precisely, climate trajectories
corresponding to different noise realizations generally cluster around a small
number of stable or transiently stable trajectories present in the
deterministic system. Furthermore, these stochastic trajectories may show
sensitive dependence on very small amounts of perturbations at key times.
Consistently with the complexity of each attractor, the number of trajectories
leaking from the clusters may range from almost zero (the model with a
quasiperiodic attractor) to a significant fraction of the total (the model with
a chaotic attractor), the models with strange nonchaotic attractors being
intermediate. Finally, we discuss the implications of this investigation for
research programmes based on numerical simulators. }Comment: Parlty based on a lecture given by M. Crucifix at workshop held in
Rome in 2013 as a part of Mathematics of Planet Earth 201
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