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Fractal Geometric Model for Statistical Intermittency Phenomenon

The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermitte...

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Autores principales: Tarraf, Walid, Queiros-Condé, Diogo, Ribeiro, Patrick, Absi, Rafik
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217421/
https://www.ncbi.nlm.nih.gov/pubmed/37238504
http://dx.doi.org/10.3390/e25050749
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author Tarraf, Walid
Queiros-Condé, Diogo
Ribeiro, Patrick
Absi, Rafik
author_facet Tarraf, Walid
Queiros-Condé, Diogo
Ribeiro, Patrick
Absi, Rafik
author_sort Tarraf, Walid
collection PubMed
description The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. To verify its ability to describe intermittency, to this model, we applied the entropic skin theory concept. This allowed us to obtain a conceptual validation. We observed that the intermittency phenomenon in our model was adequately described with the multiscale dynamics proposed by the entropic skin theory, coupling the fluctuation levels that extended between two extremes: the bulk and the crest. We calculated the reversibility efficiency γ with two different methods: statistical and geometrical analyses. Both efficiency values, [Formula: see text] and [Formula: see text] , showed equality with a low relative error margin, which actually validated our suggested fractal model for intermittency. In addition, we applied the extended self-similarity (E.S.S.) to the model. This highlighted the intermittency phenomenon as a deviation from the homogeneity assumed by Kolmogorov in turbulence.
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spelling pubmed-102174212023-05-27 Fractal Geometric Model for Statistical Intermittency Phenomenon Tarraf, Walid Queiros-Condé, Diogo Ribeiro, Patrick Absi, Rafik Entropy (Basel) Article The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. To verify its ability to describe intermittency, to this model, we applied the entropic skin theory concept. This allowed us to obtain a conceptual validation. We observed that the intermittency phenomenon in our model was adequately described with the multiscale dynamics proposed by the entropic skin theory, coupling the fluctuation levels that extended between two extremes: the bulk and the crest. We calculated the reversibility efficiency γ with two different methods: statistical and geometrical analyses. Both efficiency values, [Formula: see text] and [Formula: see text] , showed equality with a low relative error margin, which actually validated our suggested fractal model for intermittency. In addition, we applied the extended self-similarity (E.S.S.) to the model. This highlighted the intermittency phenomenon as a deviation from the homogeneity assumed by Kolmogorov in turbulence. MDPI 2023-05-03 /pmc/articles/PMC10217421/ /pubmed/37238504 http://dx.doi.org/10.3390/e25050749 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Tarraf, Walid
Queiros-Condé, Diogo
Ribeiro, Patrick
Absi, Rafik
Fractal Geometric Model for Statistical Intermittency Phenomenon
title Fractal Geometric Model for Statistical Intermittency Phenomenon
title_full Fractal Geometric Model for Statistical Intermittency Phenomenon
title_fullStr Fractal Geometric Model for Statistical Intermittency Phenomenon
title_full_unstemmed Fractal Geometric Model for Statistical Intermittency Phenomenon
title_short Fractal Geometric Model for Statistical Intermittency Phenomenon
title_sort fractal geometric model for statistical intermittency phenomenon
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217421/
https://www.ncbi.nlm.nih.gov/pubmed/37238504
http://dx.doi.org/10.3390/e25050749
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