Related papers: Nonlinear Analysis of Irregular Variables
Motivated by analyzing complicated time series, nonlinear-type time-frequency analysis became an active research topic in the past decades. Those developed tools have been applied to various problems. In this article, we review those…
A technique of timescale analysis performed directly in the time domain has been developed recently. We have applied the technique to studying rapid variabilities of hard X-rays from neutron star and black hole binaries, gamma-ray bursts…
The Fourier Transform method is a popular tool to derive the rotational velocities of stars from their spectral line profiles. However, its domain of validity does not include line-profile variables with time-dependent profiles. We…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
In the analysis of variable stars, the problem of sampling is central. This article focusses on the determination of the Nyquist frequency. It is well defined in the case of regular sampling. However, the time series of variable stars…
The recent asteroseismic data from the CoRoT and Kepler missions have provided an entirely new basis for investigating stellar properties. This has led to a rapid development in techniques for analysing such data, although it is probably…
The study of anomalous electromagnetic emission in the sky is the basis of indirect searches for dark matter. It is also a powerful tool to constrain the radiative decay of active neutrinos. Until now, quantitative analyses have focused on…
The ability to automatically and robustly self-verify periodicity present in time-series astronomical data is becoming more important as data sets rapidly increase in size. The age of large astronomical surveys has rendered manual…
Spectral analysis is a powerful tool to investigate stellar properties and it has been widely used for decades now. However, the methods considered to perform this kind of analysis are mostly based on iteration among a few diagnostic lines…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical…
Radio astronomical observations have very poor signal to noise ratios, unlike in other disciplines. On the other hand, it is possible to observe the object of interest for long time intervals as well as using a wider bandwidth.…
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…
There is growing observational evidence that the irregular changes in the light curves of certain variable stars might be due to deterministic chaos. Supporting these conclusions, several simple models of non-linear oscillators have been…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
Optical quasar spectra can be used to trace variations of the fine-structure constant alpha. Controversial results that have been published in last years suggest that in addition to to wavelength calibration problems systematic errors might…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…