Related papers: Nonlinear Analysis of Irregular Variables
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
It is known that stellar differential rotation can be detected by analyzing the Fourier transform of spectral line profiles, since the ratio of the 1st- and 2nd-zero frequencies is a useful indicator. This approach essentially relies on the…
Techniques to extract information from spectra of unresolved multi-component systems are revised, with emphasis on recent developments and practical aspects. We review the cross-correlation techniques developed to deal with such spectra,…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Optical interferometry provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Through direct observation of rotationally distorted photospheres at sub-milliarcsecond scales, we are now able to…
Nonlinear radio waves modulate the plasma, scatter on the modulations, and develop an intermittent power spectrum -- perhaps. Rudiments of theory, numerical simulations, and qualitative modeling of nonlinear scattering are presented.…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. These methods have advantages compared with common Fourier techniques concerning…
The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time…
Interferometric observations of stars in late stages of stellar evolution and the impact of VLTI observations are discussed. Special attention is paid to the spectral information that can be derived from these observations and on the…
The study of quasar variability has long been seen as a way to understanding the structure of the central engine of active galactic nuclei, and as a means of verifying the morphology of the standard model. Much work has already been done on…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
The classic problem of detection of periodic signals in the presence of noise becomes much more challenging if the observation times are themselves periodic, contain large gaps, or consist of data from several different instruments. For RR…
The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
The pseudo-spectral method is proposed for following the evolution of density and velocity fluctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity…
The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost region (i.e. close to the putative super-massive…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
The disciplines of asteroseismology and extrasolar planet science overlap methodically in the branch of high-precision photometric time series observations. Light curves are, amongst others, useful to measure intrinsic stellar variability…