Fractals and multifractals are used to model hierarchical, inhomogeneous structures in several areas of astrophysics, notably the distribution of matter at various scales in the universe. Current analysis techniques used to assert fractality or multifractality and extract scaling exponents from astrophysical data, however, have significant limitations and caveats. It is pointed out that some of...

In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insu...

Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based -optimal transport problem was presented. The model considers diffusion equation enforcing balance transported masses with time-varying conductivity that evolves proportionally to flux. In this paper we present an extension time derivative grows as power-law flux exponent ?>0. A sub-linear growth (0<?<1) penalizes intensity and p...

This paper is an attempt to attain a new and profound model of the nature’s structure using a vortex-ringfractal theory (VRFT). Scientists have been trying to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev’s periodic table, which is not in contradiction to the known laws of nature. We w...

In order to describe fractal and non-fractal distributions in a unified framework analytically, we introduce 2-dimensional quantum gravity with R term. This model is obtained by adding an interaction term with a typical scale to a scale invariant system. In addition to power law distribution, this model has Weibull-like distribution in the scale region where the typical scale is meaningful. We ...

Trying to combine fractal geometry and solid modeling seems to be a contradiction in itself, In this paper a new type of 3D objects is presented that accomplishes this combination in a specific way. Objects with a fractal macro structure and a 3D solid micro structure can be specified and rendered efficiently by using context free, attribute, geometric grammars. This new object type can be inco...

We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

BACKGROUND AND AIMS Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis o...

For fractal-like agglomerates with volume fractal dimensions Df ≤ 2 multiple scattering of incident light may be neglected to a good approximation. Therefore the Rayleigh-Debye-Gans (RDG) theory provides a reliable yet convenient route towards computing the differential and total scattering cross sections of fractal particles (Sorensen, 2001). So far, however, besides assuming spherical isotrop...