Related papers: Angular Projections of Fractal Sets
The conjecture that dark matter in galaxies is mostly cold fractal gas is developed in the more general context of the thermodynamics of the ideal isothermal gas subject to gravitational instability. This simple gas model already contains…
The visible problem is related to the arithmetic on the fractals. The visibility of self-similar set has been studied in the past. In this work, we investigate the visibility of non-self-similar sets. We begin by analyzing the structure of…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
One of the most well known random fractals is the so-called Fractal percolation set. This is defined as follows: we divide the unique cube in $\mathbb{R}^d$ into $M^d$ congruent sub-cubes. For each of these cubes a certain retention…
Recent studies have shown that massive galaxies in the distant universe are surprisingly compact, with typical sizes about a factor of three smaller than equally massive galaxies in the nearby universe. It has been suggested that these…
Galaxy clusters identified with optical imaging tend to suffer from projection effects, which impact richness (the number of member galaxies in a cluster) and lensing coherently. Physically unassociated galaxies can be mistaken as cluster…
Simple analytic arguments are used to understand the predominantly filamentary web in the large-scale distribution of galaxies. Numerical simulations of superclusters are performed to assess the feasibility of directly mapping the…
Magnetic fields play a critical role in the propagation of charged cosmic rays. Particular field configurations supported by different astrophysical objects may be observable in cosmic ray maps. We consider a simple configuration, a…
We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various…
The cosmological utility of galaxy cluster catalogues is primarily limited by our ability to calibrate the relation between halo mass and observable mass proxies such as cluster richness, X-ray luminosity or the Sunyaev-Zeldovich signal.…
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to…
We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image. We give a self-contained treatment of this bound and…
The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have…
Gravitational lensing has emerged as a powerful probe of the matter distribution on subgalactic scales, which itself may contain important clues about the fundamental origins and properties of dark matter. Broadly speaking, two different…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
This paper primarily addresses the question of whether recent lensing observations probing the small scale structure in the universe are consistent with the LCDM model. A conservative approach is taken where only the most difficult to…
We present a general relativistic description of galaxy clustering in a FLRW universe. The observed redshift and position of galaxies are affected by the matter fluctuations and the gravity waves between the source galaxies and the…
The Cold Dark Matter theory of gravitationally-driven hierarchical structure formation has earned its status as a paradigm by explaining the distribution of matter over large spans of cosmic distance and time. However, its central tenet,…
The probability distribution of lens image separations is calculated for the ``standard'' gravitational lensing statistics model in an arbitrary, flat Robertson-Walker universe, where lensing galaxies are singular isothermal spheres that…
Axisymmetric density distributions are constructed which are invisible when viewed from a range of inclination angles $i$. By adding such distributions to a model galaxy, it can be made either disky or boxy without in any way affecting its…