We use the fractional integrals to describe fractal media. We consider the fractal media as special (”fractional”) continuous media. We discuss the possible experimental testing of the continuous medium model for fractal media that is suggested in Phys. Lett. A. 336 (2005) 167-174. This test is connected with measure of period of the Maxwell pendulum with fractal medium cylinder. PACS: 03.40.-t...

We consider a simple random walk on the T-fractal and we calculate the exact mean time taug to first reach the central node i0. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except i0. By means of analytic techniques based on decimation procedures, we find the explicit express...

The aim of this paper is to provide a survey on results and future perspectives of the project “Development an validation of a sea surface fractal model” approved by ESA in the framework of the “Opportunity of exploiting ENVISAT data”. The goal is to validate a sea surface fractal model, developed by the University of Pisa, trough the use of sea SAR images. New image fractal analysis techniques...

On the basis of similar structure of solution for a second-order linear differential equation’s boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porou...

It is pointed out that the entropies of structure, information and the effectiveness entropy between knowledge and organization structure are main entropy sources of supply chain network in this paper. Firstly, establish entropy model of fractal supply chain network organization structure. Secondly, fractal knowledge management network outside independently organization structure is set up. Mor...

Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension Df 1⁄4 2:15 0:15. We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is \2.3. A kinetic model of sandblasting is presented, which...

The capillary pressure model proposed empirically by Brooks and Corey has been used widely for several decades. However it is not clear why the Brooks-Corey capillary pressure model works so well. In this study, it has been found that the empirical Brooks-Corey capillary pressure model can be derived theoretically from fractal modeling of porous media. Also found was the correlation between the...

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in R with arbitrary dimension H. Each IFS defines a probability distribution on R , so that the fractal inverse problem can b...

We study random recursive constructions with finite “memory” in complete metric spaces and the Hausdorff dimension of the generated random fractals. With each such construction and any positive number β we associate a linear operator V (β) in a finite dimensional space. We prove that under some conditions on the random construction the Hausdorff dimension of the fractal coincides with the value...

Approximation of natural objects (curves, surfaces, or images) with fractal models is an important center of interest for research. The general inverse problem paradigm concerns many application fields and a large variety of studies have been proposed to address it.The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking, these techniques lack of ...