Related papers: Interval estimation of the mass fractal dimension …
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also…
We study the scaling of the average cluster size and percolation strength of geometrical clusters for the two-dimensional Ising model. By means of Monte Carlo simulations and a finite-size scaling analysis we discuss the appearance of…
Central place systems have been demonstrated to possess self-similar patterns in both the theoretical and empirical perspectives. A central place fractal can be treated as a monofractal with a single scaling process. However, in the real…
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…
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
We build a multifractal object and use it as a support to study percolation. We identify some differences between percolation in a multifractal and in a regular lattice. We use many samples of finite size lattices and draw the histogram of…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…
We use fractional integrals to generalize the description of hydrodynamic accretion in fractal media. The fractional continuous medium model allows the generalization of the equations of balance of mass density and momentum density. These…
The statistical analysis of cosmic large-scale structure is most often based on simple two-point summary statistics, like the power spectrum or the two-point correlation function of a sample of galaxies or other types of tracers. In…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
The upper estimate of the percolation threshold of the Bernoulli random field on the hexagonal lattice is found. It is done on the basis of the cluster decomposition. Each term of the decomposition is estimated using the number estimate of…
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…
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…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation…
The anisotropy parameter of two-dimensional equilibrium clusters of site percolation process in long-range self-affine correlated structures are studied numerically. We use a fractional Brownian Motion(FBM) statistic to produce both…
The percolation of Kandel, Ben-Av and Domany clusters for 2d fully frustrated Ising model is extensively studied through numerical simulations. Critical exponents, cluster distribution and fractal dimension of percolative cluster are given.