Related papers: Angular Projections of Fractal Sets
For a wide variety of cosmological models characterized by the cosmic mass density $\Omega_M$ and the normalized cosmological constant $\Omega_{\Lambda}$, we derive an analytic expression for the estimate of magnification cross-sections by…
In the multi-fractal analysis of large scale matter distribution, the scale of transition to homogeneity is defined as the scale above which the fractal dimension of underlying point distribution is equal to the ambient dimension of the…
Self-projective sets are natural fractal sets which describe the action of a semigroup of matrices on projective space. In recent years there has been growing interest in studying the dimension theory of self-projective sets, as well as…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic…
The magnifications of the images in a strong gravitational lens system are sensitive to small mass clumps in the lens potential; this effect has been used to infer the amount of substructure in galaxy dark matter halos. I study the theory…
We extend Falconer's 1988 landmark result on the dimensions of self-affine fractals to encompass the dimensions of their projections, showing furthermore that their families of exceptional projections contain algebraic varieties which are…
The distribution of mass on galaxy cluster scales is an important test of structure formation scenarios, providing constraints on the nature of dark matter itself. Several techniques have been used to probe the mass distributions of…
Strong gravitational lenses come in many forms, but are typically divided into two populations: galaxies, and groups and clusters of galaxies. The largest objects in the Universe (i.e. galaxy clusters) are highly irregular and composed of…
I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous…
A large fraction of known galaxy-lens systems require a component of external shear to explain the observed image geometries. In most cases, this shear can be attributed to a nearby group of galaxies. We discuss how the dark-matter mass…
Despite the observational evidence that the Universe appears hierarchically structured up to a distance of at least 30 Mpc/h (and possibly up to 100 Mpc/h), the fractal paradigm has not yet been recognized by the majority of cosmologists…
Galaxy clusters identified in optical imaging surveys suffer from projection effects: Physically unassociated galaxies along a cluster's line of sight can be counted as its members and boost the observed richness (the number of cluster…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
These lecture notes concentrate on a few specific topics concerning the distribution of galaxies on scales from 0.1 to nearly 1000/h Mpc. The main aim is to provide the students with the information and tools to familiarize with a few basic…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
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…
Many gravitationally lensed quasars exhibit flux ratio "anomalies" that cannot be explained under the hypothesis that the lensing potential is smooth on scales smaller than one kpc. Micro-lensing by stars is a natural source of granularity…