Results of the dielectric relaxation studies, performed for supramolecular polymer formed by N, N ′-di(2,2-dipentylheptyl)urea dissolved in carbon tetrachloride, are presented. The measurements were done for N, N ′-di(2,2-dipentylheptyl)urea concentration up to about 7% (in mole fraction) in the frequency region from 100 kHz to 100 MHz and at the temperatures from 5◦C to 50◦C. The analysis of t...

The capacity of a wireless network with fractal and hierarchical social communications is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution P (k), and we capture the direct social connection feature between two nodes with degree k1 and k2 by a joint probability distribution P (k1, k2). Firstly, f...

where N is the number of resistors. We find a generic phase transition at/3 =/3c = -1. Also, we develop a transfer matrix technique which determines all even positive moments. The thermodynamical formalism is applied to the Hilfer-Blumen hierarchy of generalized Sierpinski gasket fractal networks, and the crossover from fractal to lattice behavior is studied. At this crossover we find a sharp p...

Recent experiments showing scaling of the intrachromosomal contact probability, P(s)∼s(-1) with the genomic distance s, are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of P(s) varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling ch...

This work results from a fractal image compression based on iterated transforms and machine learning modeling. In this work an improved quasi-losses fractal coding scheme is addressed to preserve the rich features of the medical image as the domain blocks and to generate the remaining part of the image from it based on fractal transformations. Machine learning based model is used for improving ...

This paper revisits three important concepts in fractal type network traffic, namely, self-similarity (SS), long-range dependence (LRD), and local self-similarity (LSS). Based on those concepts, we address the reason why the local properties of fractional Gaussian noise (fGn) are contained in the global properties of fGn and vice versa, which may be a limitation of fGn in data traffic modeling....

A concept of "Fractal Fracture Mechanics" for HDR .(Hot Dry Rock) geothermal reservoir design has been developed as an extension of conventional rock fracture mechanics. It is suggested that this concept is successfully applicable to characterize and model subsurface fracture network in HDR geothermal reservoir. Furthermore, this modeling procedure makes it possible to evaluate the thermal ener...

We introduce an equation for protein native topology based on recent analysis of data from the Protein Data Bank and on a generalization of the Landau-Peierls instability criterion for fractals. The equation relates the protein fractal dimension df, the spectral dimension ds, and the number of amino acids N. Deviations from the equation may render a protein unfolded. The fractal nature of prote...

Although the mobility or transport parameters, such as lift drag and pitching moments for regular-shaped particulates, are widely studied, of irregular fractal-like aggregates generated by aggregation monomers is not well understood. These particulates which ubiquitous in nature, industries have very different mechanisms compared to their spherical counterpart. A high-fidelity direct simulation...