Open AccessOn the Generative Equations of Fractal Self‐Similarity in Granular Media and the Related PSD Models
Author(s) -
Martín Miguel Ángel,
Reyes Miguel,
Taguas Francisco Javier
Publication year - 2013
Publication title -
vadose zone journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.036
H-Index - 81
ISSN - 1539-1663
DOI - 10.2136/vzj2012.0207
Subject(s) - fractal , statistical physics , similarity (geometry) , property (philosophy) , generative grammar , distribution (mathematics) , fractal dimension , frame (networking) , mathematics , computer science , physics , mathematical analysis , artificial intelligence , epistemology , image (mathematics) , telecommunications , philosophy
The physical appearance of a great number of granular media shows, together with the heterogeneity of grain sizes, suggests the existence of geometrical scale invariance. This note focuses its attention on discussing how such physicoempirical property, visually perceived, can be mathematically formulated and used in the modeling of particle size distribution (PSD). Two ways of encoding that property by means of respective equations of different natures are analyzed. They lead to respective fractal particle size distribution (PSD) models coming from sources from the literature. The nature and features of the two different models are analyzed and the simulation of the PSD by means of both models are compared. In addition, the parameters that both models provide and their role in characterizing PSD are discussed. This note aims mainly to contribute to the clarification of some conceptual, methodological, and historical aspects within the frame of the fractal modeling of PSD of granular media.