On two-scale dimension and its applications
By Qura Tul Ain, Ji-Huan He. Thermal Science, 2019
209 citations recorded by the source corpus.
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.
Subfields: Safety, Risk, Reliability and Quality
View Paper: https://www.semanticscholar.org/paper/cf63a1ffff78e43331406862c56e544d4c22172b
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Citations in the corpus
- New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle (2020, background): “T tα = (61) The explanation of the two scale transform was given in [4, 5].”