The Fast Fourier Transform was applied to spatial spectrum modeling of a one-dimensional fractal (Cantor set), a two-dimensional fractal (Sierpinski carpet), and a three-dimensional fractal (Menger sponge). A spectrum is developed for different levels. The spatial spectrum was also obtained and modeled for various filling parameters. The ParaView software package was used for 3D modeling.

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of ...

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the m...

We model the 10 µm absorption spectra of nonspherical particles composed of amorphous silicate. We consider two classes of particles, compact ones and fractal aggregates composed of homogeneous spheres. For the compact particles we consider Gaussian random spheres with various degrees of non-sphericity. For the fractal aggregates we compute the absorption spectra for various fractal dimensions....

Previous multifractal spectrum theories can only reflect that an object is multifractal and few explicit expressions of f(α) can be obtained for the practical application of nonlinearity measure. In this paper, an analytical model for multifractal systems is developed by combining and improving the Jake model, Tyler fractal model and Gompertz curve, which allows one to obtain explicit expressio...

Study of a mature petroleum play in the Western Canada Sedimentary Basin (WCSB) indicates that the spatial distribution of petroleum accumulations exhibits a self-affinity characteristic. This characteristic motivated the examination of a fractal model for a quantitative description of petroleum resource spatial distribution. The proposed approach transforms the spatial information with respect...

The purpose of this study is to identify the enriched zones of Cu, Mo and Re in Nowchun Mo-Cu porphyry deposit (SE Iran) based on subsurface data and using of concentration–volume (C–V) fractal model. The C-V model illustrates four and five geochemical zones based on Mo and Cu distributions respectively and there are three geochemical populations for Re. The main mineralization for Mo, Cu and R...

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exa...

We numerically investigate the electric potential distribution over a twodimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the quasi-equipo...

The purpose of this study is to identify the effect of Ordinary Kriging (OK) and Inverse Distance Weighted (IDW) estimation methods for the delineation of mineralized zones based on subsurface data using concentration–volume (C–V) multifractal modeling in the Dardevey iron ore deposit, NE Iran. Variograms and anisotropic ellipsoid were generated for the Fe distribution by the above estimation m...