We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk $N=uL^2$ steps, i.e. are vacant. Most results obtained from numerical simulations. Unlike its higher-dimensional counterparts, this has no sharp threshold and spanning (percolation) probability is smooth function monotonically decreasing $u$. The ...

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N=1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite num...

In this paper, a fractal photonic crystal fiber (F-PCF) based on the 1st iteration of Koch fractal configuration for optical communication systems is presented. Complex structure of fractal shape is build up through replication of a base shape. Nowadays, fractal shapes are used widely in antenna topics and its usage in PCF has not been investigated yet. The purpose of this research is to compar...

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is a fractal consisting of N>>1 nodes. Our extensive numerical simulations confirm the prediction that the most efficient navigation is attained when the length r of long-range links is taken from the distribution P(r) approximately r(-alpha), where alpha=d(f) is the fractal dimension of the underly...

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N = 1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite n...

In this work, SiO2 –ZrO2 mixed oxides was prepared by the polymeric sol–gel route. The characterization of pore structure, which determines the permeation process of membrane, is of great importance. So far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...

In this paper we investigate some of the mathematical properties of meiotic recombination. Working within the framework of a genetic model with n loci, where alpha alleles are possible at each locus, we find that the proportion of all possible diploid parental genotypes that can produce a particular haploid gamete is exp[-n log(alpha(2)/[2alpha-1])]. We show that this proportion connects recomb...

A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitabl...

This work studies the problem of GPU thread mapping for a Sierpiński gasket fractal embedded in a discrete Euclidean space of n × n. A block-space map λ : Z2E 7→ Z 2 F is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log 2 log 2 (n)) time and uses no more than O(n) threads with H ≈ 1.58... being the Hausdorff dimension, making it parallel space efficient....

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardson's law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of str...