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Structural Properties of Vicsek-like Deterministic Multifractals

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russian
Horia Hulubei, National Institute of Physics and Nuclear Engineering, 77125 Magurele, Romania
Faculty of Mathematical, Physical and Natural Sciences, Sapienza University of Rome, 00185 Rome, Italy
Faculty of Science, Technical University of Cluj Napoca, North University Center of Baia Mare, Baia Mare, 430122 Maramures, Romania
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 806;
Received: 13 May 2019 / Revised: 8 June 2019 / Accepted: 15 June 2019 / Published: 18 June 2019
(This article belongs to the Special Issue Symmetry and Mesoscopic Physics)
Deterministic nano-fractal structures have recently emerged, displaying huge potential for the fabrication of complex materials with predefined physical properties and functionalities. Exploiting the structural properties of fractals, such as symmetry and self-similarity, could greatly extend the applicability of such materials. Analyses of small-angle scattering (SAS) curves from deterministic fractal models with a single scaling factor have allowed the obtaining of valuable fractal properties but they are insufficient to describe non-uniform structures with rich scaling properties such as fractals with multiple scaling factors. To extract additional information about this class of fractal structures we performed an analysis of multifractal spectra and SAS intensity of a representative fractal model with two scaling factors—termed Vicsek-like fractal. We observed that the box-counting fractal dimension in multifractal spectra coincide with the scattering exponent of SAS curves in mass-fractal regions. Our analyses further revealed transitions from heterogeneous to homogeneous structures accompanied by changes from short to long-range mass-fractal regions. These transitions are explained in terms of the relative values of the scaling factors. View Full-Text
Keywords: fractals; small-angle scattering; form factor; structural properties; dimension spectra; pair distance distribution function fractals; small-angle scattering; form factor; structural properties; dimension spectra; pair distance distribution function
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MDPI and ACS Style

Anitas, E.M.; Marcelli, G.; Szakacs, Z.; Todoran, R.; Todoran, D. Structural Properties of Vicsek-like Deterministic Multifractals. Symmetry 2019, 11, 806.

AMA Style

Anitas EM, Marcelli G, Szakacs Z, Todoran R, Todoran D. Structural Properties of Vicsek-like Deterministic Multifractals. Symmetry. 2019; 11(6):806.

Chicago/Turabian Style

Anitas, Eugen M., Giorgia Marcelli, Zsolt Szakacs, Radu Todoran, and Daniela Todoran. 2019. "Structural Properties of Vicsek-like Deterministic Multifractals" Symmetry 11, no. 6: 806.

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