Ubiquitiform in applied mechanics

Ou, Z.-C.; Li, G.-Y.; Duan, Z.-P.; Huang, F-L.

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Tytuł artykułu

Ubiquitiform in applied mechanics

Autorzy

Ou Z.-C. , Li G.-Y. , Duan Z.-P. , Huang F-L.

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Abstrakty

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.

Słowa kluczowe

ubiquitiform fractal Hausdorff dimension

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2014

Tom

Vol. 52 nr 1

Strony

37--46

Opis fizyczny

Bibliogr. 48 poz., rys.

Twórcy

autor

Ou Z.-C.

zcou@bit.edu.cn

Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China

autor

Li G.-Y.

Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China

autor

Duan Z.-P.

Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China

autor

Huang F-L.

Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China

Bibliografia

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Bibliografia

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