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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Format: | Article |
Language: | English |
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Frontiers Media S.A.
2023-12-01
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Series: | Frontiers in Physics |
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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. |
first_indexed | 2024-03-08T21:47:02Z |
format | Article |
id | doaj.art-51e464dd76fa4ea6b56c52a6a4e60b53 |
institution | Directory Open Access Journal |
issn | 2296-424X |
language | English |
last_indexed | 2024-03-08T21:47:02Z |
publishDate | 2023-12-01 |
publisher | Frontiers Media S.A. |
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series | Frontiers in Physics |
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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