Ubiquitiform in applied mechanics
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Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
Journal of Theoretical and Applied Mechanics 2014;52(1):37-46
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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