Related papers: The Confluent System Formalism: I.The Mass Functio…
With the present paper we conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instability from a random Gaussian field of density fluctuations. In paper I, we…
In order to study the statistics of the objects with hierarchical merging, we propose the skeleton tree formalism, which can analytically distinguish the episodic merging and the continuous accretion in the mass growth processes. The…
We carry out N-body simulations of several non-Gaussian structure formation models, including Peebles' isocurvature cold dark matter model, cosmic string models, and a model with primordial voids. We compare the evolution of the cluster…
I review the main steps made so far towards the construction of a (semi) analytical model for describing the growth history of bound virialized objects or haloes in the gravitational instability scenario. I mainly focus on those models…
The Press-Schechter(PS) formalism for the mass function of the collapsed objects are reanalyzed. The factor of two in the Press-Schechter formalism is argued to be correct in the sharp $k$-space filter even when we use the another approach…
The Press-Schechter (PS) formalism for mass functions of the gravitationally collapsed objects is reanalyzed. It has been suggested by many authors that the PS mass function agrees well with the mass function given by $N$-body simulations,…
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…
We compare the mass functions obtained analytically, in the framework of an extended Press & Schechter (PS) formalism, in a previous paper to the numerical mass functions obtained in N -- body simulations, using different algorithms to…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight…
Aims. We aim to study the stochastic evolution of the smoothed overdensity $\delta$ at scale $S$ of the form $\delta(S) = \int_{0}^S K(S,u)\mathrm{d}W(u)$, where $K$ is a kernel and $\mathrm{d}W$ is the usual Wiener process. Methods. For a…
The formalism by Press and Schechter (PS) is often used to infer number densities of virialized objects of mass M (e.g. quasars, galaxies, clusters of galaxies, etc.) from a count of initially overdense regions in a Gaussian density…
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed…
We revisit the cloud-in-cloud problem for non-Gaussian density fluctuations. We show that the extended Press-Schechter (EPS) formalism for non-Gaussian fluctuations has a flaw in describing mass functions regardless of type of filtering. As…
(shortened) We develop and test a method to compute mass and auto-correlation functions of rich clusters of galaxies from linear density fluctuations, based on the formalism of Gaussian peaks (Bardeen et al 1986). The essential, new…
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…
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution…
The observed abundance of high-redshift galaxies and clusters contains precious information about the properties of the initial perturbations. We present a method to compute analytically the number density of objects as a function of mass…
Granular fronts are a common yet unexplained phenomenon emerging during the gravity driven free-surface flow of concentrated suspensions. They are usually believed to be the result of fluid convection in combination with particle size…
We study the merging history of dark matter haloes that end up in rich clusters, using N-body simulations of a scale-free universe. We compare the predictions of the extended Press & Schechter (PS) formalism (Bond et al. 1991; Bower 1991;…
The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has…