Related papers: Interval estimation of the mass fractal dimension …
This report focuses on the dependencies for the center and radius of the confidence interval that arise when estimating the mass fractal dimensions of isotropic sampling clusters in the site percolation model.
In this paper we study statistical methods of parameters estimation of the site percolation model. Advantages of the proposed method is demonstrated for the computing of the confidence interval of mass fractal dimension of a percolation…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
This paper deals with an estimating of the Fractal Dimension of a hydrometeorology variables like an Air temperature or humidity at a different sites in a landscape (and will be further evaluated from the land use point of view). Three…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high…
The effect of geometry and morphology of superconducting structure on magnetic flux trapping is considered. It is found that the clusters of normal phase, which act as pinning centers, have significant fractal properties. The fractal…
In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute…