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2014 | Vol. 52 nr 1 | 37--46
Tytuł artykułu

Ubiquitiform in applied mechanics

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We demonstrate that a physical object in nature should not be described as a fractal, despite an ideal mathematical object, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure). It is shown mathematically that a ubiquitiform must be of integral dimension, and that the Hausdorff dimension of the initial element of a fractal changes abruptly at the point at infinity, which results in divergence of the integral dimensional measure of the fractal and makes the fractal approximation to a ubiquitiform unreasonable. Therefore, instead of the existing fractal theory in applied mechanics, a new type of ubiquitiformal one is needed.
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Bibliogr. 48 poz., rys.
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  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
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