Related papers: Statistics of Merging Peaks of Random Gaussian Flu…
This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present…
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…
The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called `{\it merger trees}') are analysed. We compare the mass functions of dark haloes derived by a new method for calculating merger…
In two previous papers a semi-analytical model was presented for the hierarchical clustering of halos via gravitational instability from peaks in a random Gaussian field of density fluctuations. This model is better founded than the…
In hierarchical evolution, voids exhibit two different behaviors related with their surroundings and environments, they can merge or collapse. These two different types of void processes can be described by the two-barrier excursion set…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at…
After more than a century of research the typical growth pattern of a tree was thought to be fairly well understood. Following germination height growth accelerates for some time, then increment peaks and the added height each year becomes…
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,…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
We present a new method for calculating the merger history of matter halos in hierarchical clustering cosmologies. The linear density field is smoothed on a range of scales, these are then ordered in decreasing density and a merger tree…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
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…
Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…
The local extremes (i.e., peaks and pits) of the landscape-elevation field play a critical role in energy, water, and nutrient distribution over the region, but the statistical distributions of these points in relation to landscape…
The excursion set approach uses the statistics of the density field smoothed on a wide range of scales, to gain insight into a number of interesting processes in nonlinear structure formation, such as cluster assembly, merging and…
The fluctuations in the particle size distribution for processes of fragmentation and aggregation are studied for stationary state regimes. The system is described in terms of a stochastic process over an adequate tree structure. The RMS…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…