相关论文: Fractal analysis applied to light curves of $\delt…
Fractal fingerprints have been found recently in the light curves of several {\delta} Scuti stars observed by CoRoT satellite. This sole fact might pose a problem for the detection of pulsation frequencies using classical pre-whitening…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
Space missions have produced an incredibly large database on pulsating stars. The light curves via the frequency content contain a detailed description of each star. The critical point is the identification of modes, especially in the…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
$\delta$ Scuti stars are pulsating variable stars that exhibit both radial and non-radial pulsations, making them key objects for understanding stellar evolution and internal structures. The current classification of $\delta$ Scuti stars…
Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
The main obstacle in exploiting the frequency data of $\delta$ Sct stars is difficulty in mode identification. The $\delta$ Sct oscillation spectra, unlike those of the Sun or white dwarfs, do not exhibit very regular patterns. Thus, the…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Within the context of a fractal paradigm that emphasizes nature's well-stratified hierarchical organization, the delta Scuti class of variable stars is investigated for evidence of discrete cosmological self-similarity. Methods that were…
The phenomenology associated with line profile variations in delta Scuti stars is reviewed. The three main techniques adopted to detect pulsation modes, i.e., the pixel-by-pixel analysis, the analysis of the moment time series and the…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
Detecting and understanding rotation in stellar interiors is nowadays one of the unsolved problems in stellar physics. Asteroseismology has been able to provide insights on rotation for the Sun, solar-like stars, and compact objects like…