Universal fractality of morphological transitions in stochastic growth processes

Universal fractality of morphological transitions in stochastic growth processes

Abstract Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: J. R. Nicolás-Carlock, J. L. Carrillo-Estrada, V. Dossetti
Formato: article
Lenguaje:EN
Publicado: Nature Portfolio 2017
Materias:
Medicine
R
Science
Q
Acceso en línea:https://doaj.org/article/a7cd5650876749fd88a580dfaaae7d9c
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
id oai:doaj.org-article:a7cd5650876749fd88a580dfaaae7d9c
record_format dspace
spelling oai:doaj.org-article:a7cd5650876749fd88a580dfaaae7d9c2021-12-02T11:40:34ZUniversal fractality of morphological transitions in stochastic growth processes10.1038/s41598-017-03491-52045-2322https://doaj.org/article/a7cd5650876749fd88a580dfaaae7d9c2017-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-03491-5https://doaj.org/toc/2045-2322Abstract Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.J. R. Nicolás-CarlockJ. L. Carrillo-EstradaV. DossettiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
J. R. Nicolás-Carlock
J. L. Carrillo-Estrada
V. Dossetti
Universal fractality of morphological transitions in stochastic growth processes
description Abstract Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.
format article
author J. R. Nicolás-Carlock
J. L. Carrillo-Estrada
V. Dossetti
author_facet J. R. Nicolás-Carlock
J. L. Carrillo-Estrada
V. Dossetti
author_sort J. R. Nicolás-Carlock
title Universal fractality of morphological transitions in stochastic growth processes
title_short Universal fractality of morphological transitions in stochastic growth processes
title_full Universal fractality of morphological transitions in stochastic growth processes
title_fullStr Universal fractality of morphological transitions in stochastic growth processes
title_full_unstemmed Universal fractality of morphological transitions in stochastic growth processes
title_sort universal fractality of morphological transitions in stochastic growth processes
publisher Nature Portfolio
publishDate 2017
url https://doaj.org/article/a7cd5650876749fd88a580dfaaae7d9c
work_keys_str_mv AT jrnicolascarlock universalfractalityofmorphologicaltransitionsinstochasticgrowthprocesses
AT jlcarrilloestrada universalfractalityofmorphologicaltransitionsinstochasticgrowthprocesses
AT vdossetti universalfractalityofmorphologicaltransitionsinstochasticgrowthprocesses
_version_ 1718395600535289856

Ejemplares similares