This paper demonstrates that the absorption and scattering cross-sections and the asymmetry factor of randomly oriented fractal aggregates of spherical monomers can be rapidly estimated as those of coated spheres with equivalent volume and average projected area. This was established for fractal aggregates with fractal dimension ranging from 2.0 to 3.0 and composed of up to 1000 monodisperse or...

Fractal analyses have become very popular and have been applied on a wide variety of empirical time series. The application of these methods supposes that the monofractal framework can offer a suitable model for the analyzed series. However, this model takes into account a quite specific kind of fluctuations, and we consider that fractal analyses have been often applied to series that were comp...

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic...

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic...

The author reviews visual perception studies showing that fractal patterns possess an aesthetic quality based on their visual complexity. Specifically, people display an aesthetic preference for patterns with mid-range fractal dimensions, irrespective of the method used to generate them. The author builds upon these studies by presenting preliminary research indicating that mid-range fractals a...

A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the ap...

[1] Box counting is widely used for characterizing fracture networks as fractals and estimating their fractal dimensions (D). If this analysis yields a power law distribution given by N / r , where N is the number of boxes containing one or more fractures and r is the box size, then the network is considered to be fractal. However, researchers are divided in their opinion about which is the bes...

the subject of geometry and proportions has been regarded as an issue which has a close relationship with architecture. since the entire universe, living beings and the human geometry can be seen clearly, that’s why our unconscious essence has accustomed to these proportions whereby reflection of this mentality can be seen in the architect’s hands and thought in the architecture. it can witness...

the ardabil geothermal area is located in the northwest of iran, which hosts several hot springs. it is situated mostly around the sabalan mountain. the sabalan geothermal area is now under investigation for the geothermal electric power generation. it is characterized by its high thermal gradient and high heat flow. in this study, our aim is to determine the fractal parameter and top and botto...

One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dime...