Peculiarities of wave scattering by fat fractals

Bulgakov, S. A.

doi:10.1103/physreva.46.8024

Cited by 6 publications

(2 citation statements)

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“…Their main peculiarity, compared to thin fractals, consists in a finite and non-zero Lebesgue measure of their support. The empty holes of fat fractals have size-dependant power distribution similar to porous materials [3,14] and they have been proposed as realistic models of micro-porous media [3], Let us recall how a 1-D regular fat fractal is generated. For sake of simplicity, we usually use the unit interval as initiator.…”

Section: Fractal-like Texture Fat Fractals: Synthetic Porous Mediamentioning

confidence: 99%

“…For example, the design of synthetic polymers has been revolutionized by the new achievements in high-resolution, broad-mass-range spectrometry [1]. Wave propagation and scattering through porous media and highly ramified materials lead to (spatial) signals which can be considered as defined on fractal systems [2,3]. As a matter of fact, the obtained mass spectra, which carry out microstructure information of great impact on the macroscopic physical properties, can be very complex.…”

Section: Introductionmentioning

confidence: 99%

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Various Mathematical Approaches to Extract Information from Textures of Increasing Complexities

Nekka

Fractals in Engineering

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Summary. Dealing with several structures of different complexities, we adopt various strategies to extract information. The general idea is to find appropriate tools to analyze the variation of the corresponding autocorrelation functions. First, for homogeneous media under different conditions, we recover, in a statistical way, a relationship between porosity and the autocorrelation function. Then, for low-complexity textures, we exploit this relationship to extract complementary parameters from the autocorrelation function beyond porosity using spectral analysis. For fractal-like structures, we process them according to their porosity. For fat fractals,usually used as synthetic models of porous media, we combine the regularization dimension, a method proposed to estimate the curve variation, with the autocorrelation function. This leads to a more robust classification. For fractals of negligible porosity, such as fractals of non-integer dimension, we discuss how the method HMSF we developed serves as an original means to estimate the Hausdorff dimension and how it can be exploited to give complementary characteristic parameters.

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Section: Fractal-like Texture Fat Fractals: Synthetic Porous Mediamentioning

confidence: 99%