Related papers: Quantitative Analysis of Voids in Percolating Stru…
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…
We critically examine how well the evolution of large-scale density perturbations is followed in cosmological $N$-body simulations. We first run a large volume simulation and perform a mode-by-mode analysis in three-dimensional Fourier…
We study scaling behaviour of statistics of voids in the context of the halo model of nonlinear large-scale structure. The halo model allows us to understand why the observed galaxy void probability obeys hierarchical scaling, even though…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
Cosmic voids, the large underdense regions of our Universe, have emerged over the past decade as powerful cosmological laboratories: their simple dynamics, sensitivity to local gravitational effects and cosmic expansion, and ability to span…
Contrary to the common view voids have very complex internal structure and dynamics. Here we show how the hierarchy of structures in the density field inside voids is reflected by a similar hierarchy of structures in the velocity field.…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
We report the {\em first} systematic study of the supercluster-void network in the $\Lambda$CDM concordance cosmology treating voids and superclusters on an equal footing. We study the dark matter density field in real space smoothed with…
We review and discuss aspects of Cosmic Voids that form the background for our Void Galaxy Survey (see accompanying paper by Stanonik et al.). Following a sketch of the general characteristics of void formation and evolution, we describe…
Halo models of the large scale structure of the Universe are critically examined, focusing on the definition of halos as smooth distributions of cold dark matter. This definition is essentially based on the results of cosmological N-body…
In a Monte Carlo study the conductivity of two-dimensional random stick systems is investigated from the percolation threshold up to ten times the percolation threshold density. We propose a model explicitly depending on the stick density…
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…
For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…
We present in this article an analysis of some of the properties of the density field realized in numerical simulations for power-law initial power-spectra in the case of a critical density universe. We compare our numerical results in the…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
Size segregation in granular flows is a well-known phenomenon: laboratory experiments consistently show that large particles migrate toward silo walls during filling, while smaller particles concentrate near the center. Paradoxically, field…
Two-dimensional bootstrap percolation is usually characterized by bulk observables, but whether increasing the activation threshold qualitatively reorganizes the geometry of the absorbing state has remained unclear. Here we show that the…
We present a non-parametric, model-independent method to reconstruct the spherical density profiles of void stacks in real space, without redshift-space distortions. Our method uses the expected spherical symmetry of stacked voids to build…
A novel method allowing to compute density, velocity and other fields in cosmological N--body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold…