Related papers: Frequently asked questions about fractals
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…
In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to…
To understand galaxies and their evolution, it is necessary to describe how the different scales interact: how the microscopic physics, such as star formation, or the large scale physics, such as galaxy interactions may modify the galaxy…
Recent multifrequency observations contribute to derive a comprehensive picture of the origin and evolution of relativistic particles in galaxy clusters. In this review I briefly discuss theoretical aspects and open problems of this…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…
These notes provide an introduction to the theory of the formation and early evolution of planetary systems. Topics covered include the structure, evolution and dispersal of protoplanetary disks; the formation of planetesimals, terrestrial…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
In these three lectures a review is provided of the properties of galaxy systems as determined from optical and infrared measurements. Covered topics are: clusters identification, global cluster properties and their scaling relations,…
We present a review of the history and the present state of the fractal approach to the large-scale distribution of galaxies. Angular correlation function was used as a general instrument for the structure analysis. It was realized later…
Galaxy clusters are sources of gravitational radiation. The main aim of this paper is to give numerical estimates and theoretical description of the relevant features of the gravitational radiation coming from an appropriate spatial…
I review the standard paradigm for understanding the formation and evolution of cosmic structure, based on the gravitational instability of dark matter, but many variations on this basic theme are viable. Despite the great progress that has…
Several issues related to the gravitational clustering of collisionless dark matter in an expanding universe is discussed. The discussion is pedagogical but the emphasis is on semianalytic methods and open questions - rather than on well…
I review at the non-specialist level recent progress in the study of the large-scale structure of the Universe, covering the following areas: (1) Results from recently completed or ongoing redshift surveys of galaxies and X-ray clusters;…
In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on…
The clustering of galaxies is well characterized by fractal properties, with the presence of an eventual cross-over to homogeneity still a matter of considerable debate. In this letter we discuss the cosmological implications of a fractal…
We review knowledge of galaxy structures obtained by their emitted light and in the local universe where they can be studied in great detail. We discuss the shapes of, and stellar motions within, galaxies, compositional clues derived from…
These lectures describe some of the latest data on particle production in high-energy collisions and compare them with theoretical calculations and models based on QCD. The main topics covered are: fragmentation functions and factorization,…