Open AccessSome Notes on Granular Mixtures with Finite, Discrete Fractal Distribution
Author(s) -
E. Imre,
István Talata,
Daniel Barreto,
Maria Datcheva,
Wiebke Baille,
Ivan Georgiev,
Stephen Fityus,
Vijay P. Singh,
Francesca Casini,
Giulia Guida,
Phong Q. Trang,
János Lörincz
Publication year - 2021
Publication title -
periodica polytechnica. civil engineering/periodica polytechnica. civil engineering (online)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.406
H-Index - 19
eISSN - 1587-3773
pISSN - 0553-6626
DOI - 10.3311/ppci.19103
Subject(s) - fractal dimension , fractal , mathematics , fractal dimension on networks , entropy (arrow of time) , geometry , fractal analysis , mathematical analysis , multifractal system , statistical physics , grading (engineering) , physics , thermodynamics , civil engineering , engineering
Why fractal distribution is so frequent? It is true that fractal dimension is always less than 3? Why fractal dimension of 2.5 to 2.9 seems to be steady-state or stable? Why the fractal distributions are the limit distributions of the degradation path? Is there an ultimate distribution? It is shown that the finite fractal grain size distributions occurring in the nature are identical to the optimal grading curves of the grading entropy theory and, the fractal dimension n varies between –¥ and ¥. It is shown that the fractal dimensions 2.2–2.9 may be situated in the transitional stability zone, verifying the internal stability criterion of the grading entropy theory. Micro computed tomography (μCT) images and DEM (distinct element method) studies are presented to show the link between stable microstructure and internal stability. On the other hand, it is shown that the optimal grading curves are mean position grading curves that can be used to represent all possible grading curves.