Related papers: Frequently asked questions about fractals
This is the first in a series of papers that analyze college student beliefs in realms where common astronomy misconceptions are prevalent. Data was collected through administration of an inventory distributed at the end of an introductory…
In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. This is followed by lectures on important…
We provide a brief summary of the history of galaxy structure studies. We also introduce several large-scale redshift surveys and summarize the most commonly used methods to identify the groups and clusters of galaxies. We present several…
The interstellar medium is structured as a hierachy of gas clouds, that looks self-similar over 6 orders of magnitude in scales and 9 in masses. This is one of the more extended fractal in the Universe. At even larger scales, the ensemble…
Gapless fracton phases are characterized by the conservation of certain charges and their higher moments. These charges generically couple to higher rank gauge fields. In this paper we study systems conserving charge and dipole moment, and…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
Gravitational Lensing is a UNIQUE tool to constrain the mass distribution of collapsed structures, this is particularly true for galaxies, either on a case by case basis using multiple images of background sources (such as quasars), or…
The lecture introduces a trous wavelet transforms, explains how to estimate the spatial density for galaxy distributions, and, finally, how to describe the morphology of cosmological density fields. An example application of these methods…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each…
These lectures cover the basics of inflationary models for the early universe, concentrating particularly on the generation of density fluctuations from scalar-field dynamics. The subsequent gravitational dynamics of these fluctuations in…
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the…
Interacting galaxies are a natural arena for studies of non-equilibrium stellar dynamics, gas dynamics, and thermodynamics. Only galaxy formation itself is as deeply concerned with as many different aspects of dynamics, and the connection…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
These lectures summarize our basic understanding of the emergence of cosmic structures, the epoch of first light, the survival of early substructure in present-day galaxy halos.
Rich clusters of galaxies are the most massive virialized systems known. Even though they contain only a small fraction of all galaxies, rich clusters provide a powerful tool for the study of galaxy formation, dark matter, large-scale…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…