THERMAL SCIENCE

International Scientific Journal

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Qura Tul Ain

,

Ji-Huan He

ON TWO-SCALE DIMENSION AND ITS APPLICATIONS

ABSTRACT
Dimension or scale is everything. When a thing is observed by different scales, different results can be obtained. Two scales are enough for most of practical problems, and a new definition of a two-scale dimension instead of the fractal dimension is given to deal with discontinuous problems. Fractal theory considers a self-similarity pattern, which cannot be found in any a real problem, while the two-scale theory observes each problem with two scales, the large scale is for an approximate continuous problem, where the classic calculus can be fully applied, and on the smaller scale, the effect of the porous structure on the properties can be easily elucidated. This paper sheds a new light on applications of fractal theory to real problems.
KEYWORDS
fractal calculus, fractal dimension, two-scale dimension, two-scale transform, fractal Fourier's law, hierarchical structure, magic, uncertainty
PAPER SUBMITTED: 2019-04-08
PAPER REVISED: 2019-04-09
PAPER ACCEPTED: 2019-04-09
PUBLISHED ONLINE: 2019-04-14
DOI REFERENCE: https://doi.org/10.2298/TSCI190408138A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 3, PAGES [1707 - 1712]
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On two-scale dimension and its applications

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence