Related papers: Nonlinear Analysis of Irregular Variables
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…
Measuring neutron star radii with spectroscopic and timing techniques relies on the combination of multiple observables to break the degeneracies between the mass and radius introduced by general relativistic effects. Here, we explore a…
The aim of this article is to demonstrate the useful role that can be played by spectropolarimetric observations of young and evolved emission line stars that analyse the linearly polarized component in their spectra. At the time of…
We investigate astrophysical contributions to the statistical uncertainty of precision radial velocity measurements of stellar spectra. We analytically determine the uncertainty in centroiding isolated spectral lines broadened by Gaussian,…
CONTEXT: Spectral-line asymmetries and wavelength shifts are signatures of hydrodynamics in solar and stellar atmospheres. Theory may precisely predict idealized lines, but observed spectra are limited by blends, too few suitable lines,…
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Emission lines in ionized nebulae can provide strong and useful constraints on the properties of both ionizing and non-ionizing stellar populations in regions with star formation, provided that stellar evolution and stellar atmosphere…
Additional pulsation modes have been discovered in many Cepheids, RR Lyrae, and other variable stars. Fourier transforms are used to find, fit and subtract the main pulsation period and its harmonics to reveal additional modes. Commonly,…
Calculations are performed for the linear polarization of starlight due to extinction by aligned dust grains when the starlight traverses a medium with irregular magnetic fields. This medium is intended to represent the optically thick…
The advent of new time domain surveys and the imminent increase in astronomical data expose the shortcomings in traditional time series analysis (such as power spectra analysis) in characterising the abundantly varied, complex and…
Stars exhibit a bewildering variety of variable behaviors ranging from explosive magnetic flares to stochastically changing accretion to periodic pulsations or rotations. The principal LSST surveys will have cadences too sparse and…
Asteroseismology has the capability of delivering stellar properties which would otherwise be inaccessible, such as radii, masses and thus ages of stars. When coupling this information with classical determinations of stellar parameters,…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example,…
We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics…