Related papers: Interval estimation of the mass fractal dimension …
We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as…
In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…
For three different geometric configurations of matter and two different thermodynamic equations of state, low angular momentum, multi-transonic, axially symmetric accretion flow of matter having fractional dimension of mass distribution…
This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
In recent paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and…
Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners''…
We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and fractal percolation. In each setting we compute either the \emph{almost sure} or the \emph{Baire…
Conformal mapping models are used to study competition of noise and anisotropy in Laplacian growth. For that, a new family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is…
We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin…
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four…
This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation and the Minimal Spanning Tree. We show here…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents…
We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the non-trapping invasion percolation model indicate that…
The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The…
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…