Decomposing the percolation backbone reveals novel scaling laws of the current distribution

The distribution of currents on critical percolation clusters is the fundamental quantity describing the transport properties of weakly connected systems. Nevertheless, its finite-size extrapolation is still one of the outstanding open questions concerning disordered media. By hierarchically decompo...

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Main Authors: Wagner R. de Sena, José S. Andrade, Hans J. Herrmann, André A. Moreira
Format: Article
Language:English
Published: Frontiers Media S.A. 2023-12-01
Series:Frontiers in Physics
Subjects:
Online Access:https://www.frontiersin.org/articles/10.3389/fphy.2023.1335339/full
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author Wagner R. de Sena
José S. Andrade
Hans J. Herrmann
Hans J. Herrmann
André A. Moreira
author_facet Wagner R. de Sena
José S. Andrade
Hans J. Herrmann
Hans J. Herrmann
André A. Moreira
author_sort Wagner R. de Sena
collection DOAJ
description The distribution of currents on critical percolation clusters is the fundamental quantity describing the transport properties of weakly connected systems. Nevertheless, its finite-size extrapolation is still one of the outstanding open questions concerning disordered media. By hierarchically decomposing the 3-connected components of the backbone, we disclose that the current distribution is determined from two distributions, namely, the one corresponding to the number of bonds in each level and another one corresponding to the factors by which the current is reduced, when going from one level to the next. The first distribution follows a finite-size scaling, while the second is a power law with an exponent consistent with 3/4 in two dimensions. The standard hierarchical model for the backbone is too simple to reproduce this complex scenario. Our new decomposition method of the backbone also allows to calculate much smaller currents than before, attaining a precision of 10−35 and systems of size L = 81922. Moreover, our method is not restricted to electric currents on critical percolation clusters but could also be applied to other transport problems on sparse graphs including fluid flow and car traffic.
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spelling doaj.art-51e464dd76fa4ea6b56c52a6a4e60b532023-12-20T08:12:59ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-12-011110.3389/fphy.2023.13353391335339Decomposing the percolation backbone reveals novel scaling laws of the current distributionWagner R. de Sena0José S. Andrade1Hans J. Herrmann2Hans J. Herrmann3André A. Moreira4Departamento de Física, Universidade Federal do Ceará, Fortaleza, BrazilDepartamento de Física, Universidade Federal do Ceará, Fortaleza, BrazilDepartamento de Física, Universidade Federal do Ceará, Fortaleza, BrazilPMMH, ESPCI, CNRS UMR 7636, Paris, FranceDepartamento de Física, Universidade Federal do Ceará, Fortaleza, BrazilThe distribution of currents on critical percolation clusters is the fundamental quantity describing the transport properties of weakly connected systems. Nevertheless, its finite-size extrapolation is still one of the outstanding open questions concerning disordered media. By hierarchically decomposing the 3-connected components of the backbone, we disclose that the current distribution is determined from two distributions, namely, the one corresponding to the number of bonds in each level and another one corresponding to the factors by which the current is reduced, when going from one level to the next. The first distribution follows a finite-size scaling, while the second is a power law with an exponent consistent with 3/4 in two dimensions. The standard hierarchical model for the backbone is too simple to reproduce this complex scenario. Our new decomposition method of the backbone also allows to calculate much smaller currents than before, attaining a precision of 10−35 and systems of size L = 81922. Moreover, our method is not restricted to electric currents on critical percolation clusters but could also be applied to other transport problems on sparse graphs including fluid flow and car traffic.https://www.frontiersin.org/articles/10.3389/fphy.2023.1335339/fullpercolationmultifractaltransport phenomenafinite-size scaling analysisself-similar (fractal) systems
spellingShingle Wagner R. de Sena
José S. Andrade
Hans J. Herrmann
Hans J. Herrmann
André A. Moreira
Decomposing the percolation backbone reveals novel scaling laws of the current distribution
Frontiers in Physics
percolation
multifractal
transport phenomena
finite-size scaling analysis
self-similar (fractal) systems
title Decomposing the percolation backbone reveals novel scaling laws of the current distribution
title_full Decomposing the percolation backbone reveals novel scaling laws of the current distribution
title_fullStr Decomposing the percolation backbone reveals novel scaling laws of the current distribution
title_full_unstemmed Decomposing the percolation backbone reveals novel scaling laws of the current distribution
title_short Decomposing the percolation backbone reveals novel scaling laws of the current distribution
title_sort decomposing the percolation backbone reveals novel scaling laws of the current distribution
topic percolation
multifractal
transport phenomena
finite-size scaling analysis
self-similar (fractal) systems
url https://www.frontiersin.org/articles/10.3389/fphy.2023.1335339/full
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