Structural investigations of fat fractals using small-angle scattering

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Anitas, Eugen M.^1,2

Joint Institute for Nuclear Research, Moscow region, Dubna

141980, Russia^1

Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest

RO-077125, Romania^2

关键词: Fractal structures;    Lebesgue measure;    Logarithmic scale;    Small angle scattering;    Structural information;    Structural investigation;    Structural levels;    Theoretical modeling;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012093/pdf
DOI  :  10.1088/1742-6596/574/1/012093

来源: IOP

【 摘 要 】

Experimental small-angle scattering (SAS) data characterized, on a double logarithmic scale, by a succession of power-law decays with decreasing values of scattering exponents, can be described in terms of fractal structures with positive Lebesgue measure (fat fractals). Here we present a theoretical model for fat fractals and show how one can extract structural information about the underlying fractal using SAS method, for the well known fractals existing in the literature: Vicsek and Menger sponge. We calculate analytically the fractal structure factor and study its properties in momentum space. The models allow us to obtain the fractal dimension at each structural level inside the fractal, the number of particles inside the fractal and about the most common distances between the center of mass of the particles.