Related papers: Probing Large Scale Structure using Percolation an…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
Large-scale structure of the universe is a useful cosmological probe of the primordial non-Gaussianity and the expansion history of the universe because its topology does not change with time in the linear regime in the standard paradigm of…
Catalogues of galaxies, clusters of galaxies and superclusters - sources of information to study the large-scale structure of the Universe are reviewed. The power spectrum of density perturbations, and the correlation function are discussed…
The genus of the iso-density contours is a robust measure of the topology of large scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias and redshift-space distortion. We show that the growth of…
The topology of large scale structure is studied as a function of galaxy type using the genus statistic. In hydrodynamical cosmological CDM simulations, galaxies form on caustic surfaces (Zeldovich pancakes) then slowly drain onto filaments…
As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a…
We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of…
The gravitational evolution of the genus and other statistics of isodensity contours of the density field is derived analytically in a weakly nonlinear regime using second-order perturbation theory. The effect of final smoothing in…
Even as our measurements of cosmological parameters improve, the physical nature of the dark sector of the universe largely remains a mystery. Many effects of dark sector models are most prominent at very large scales and will rely on…
We investigate the geometric properties of percolation clusters, by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo…
Galaxies are not uniformly distributed in space. On large scales the Universe displays coherent structure, with galaxies residing in groups and clusters on scales of ~1-3 Mpc/h, which lie at the intersections of long filaments of galaxies…
We have studied the dependence of topology of large scale structure on tracer, gravitational evolution, redshift space distortion, and cosmology. A series of large N-body simulations of the $\Lambda$CDM and SCDM models that have evolved 1.1…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
The history and the major results of the study of the topology of the large-scale structure are briefly reviewed. Two techniques based on percolation theory and the genus curve are discussed. The preliminary results of the percolation…
We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to…
We study the evolution of non-linear structure as a function of scale in samples from the 2dF Galaxy Redshift Survey, constituting over 221 000 galaxies at a median redshift of z=0.11. The two flux-limited galaxy samples, located near the…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively…