Dielectric breakdown in solids modeled by DBM and DLA

Using numerical simulation, two stochastic models of electrical treeing in solid dielectrics are compared. These are the diffusion-limited aggregation (DLA) model and the dielectric breakdown model (DBM or η-model). On a linear two-dimensional geometry, the relationship between both models, when the...

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Publicado: 2002
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Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v13_n6_p1333_Irurzun
http://hdl.handle.net/20.500.12110/paper_09600779_v13_n6_p1333_Irurzun
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spelling paper:paper_09600779_v13_n6_p1333_Irurzun2023-06-08T15:57:27Z Dielectric breakdown in solids modeled by DBM and DLA Algorithms Boundary conditions Computational geometry Correlation methods Dielectric materials Fractals Mathematical models Random processes Dielectric breakdown Electric breakdown of solids Using numerical simulation, two stochastic models of electrical treeing in solid dielectrics are compared. These are the diffusion-limited aggregation (DLA) model and the dielectric breakdown model (DBM or η-model). On a linear two-dimensional geometry, the relationship between both models, when the size of the structures is of the order of the experimental samples (the electrode gap is 100 times the length of the discharge channel), is explored by statistical methods. Although there is a one-to-one correspondence between DBM with η=1 and the DLA model when the structure size is very large, the case of rather smaller structures is not well known. From a fractal analysis, employing the method of the correlation function C(r), it follows that average fractal dimension of electrical trees, generated with the DLA or with the DBM (η=1), collapse (up to the numerical uncertainty), on a single curve that "universally" accounts for finite size effects. Even more, from this analysis we conclude that the two curves obtained for DLA and DBM (η=1) cannot be distinguished if one takes into account the error bars. This means that finite size effects in the fractal analysis of DLA and DBM (η=1) are quite the same (despite the differences in the algorithms respectively used to generate the electrical trees). To our knowledge no comparison has ever been made between the similarities and differences of the DBM and DLA approach on a geometry other than the open-planar geometry. © 2002 Elsevier Science Ltd. All rights reserved. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v13_n6_p1333_Irurzun http://hdl.handle.net/20.500.12110/paper_09600779_v13_n6_p1333_Irurzun
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Algorithms
Boundary conditions
Computational geometry
Correlation methods
Dielectric materials
Fractals
Mathematical models
Random processes
Dielectric breakdown
Electric breakdown of solids
spellingShingle Algorithms
Boundary conditions
Computational geometry
Correlation methods
Dielectric materials
Fractals
Mathematical models
Random processes
Dielectric breakdown
Electric breakdown of solids
Dielectric breakdown in solids modeled by DBM and DLA
topic_facet Algorithms
Boundary conditions
Computational geometry
Correlation methods
Dielectric materials
Fractals
Mathematical models
Random processes
Dielectric breakdown
Electric breakdown of solids
description Using numerical simulation, two stochastic models of electrical treeing in solid dielectrics are compared. These are the diffusion-limited aggregation (DLA) model and the dielectric breakdown model (DBM or η-model). On a linear two-dimensional geometry, the relationship between both models, when the size of the structures is of the order of the experimental samples (the electrode gap is 100 times the length of the discharge channel), is explored by statistical methods. Although there is a one-to-one correspondence between DBM with η=1 and the DLA model when the structure size is very large, the case of rather smaller structures is not well known. From a fractal analysis, employing the method of the correlation function C(r), it follows that average fractal dimension of electrical trees, generated with the DLA or with the DBM (η=1), collapse (up to the numerical uncertainty), on a single curve that "universally" accounts for finite size effects. Even more, from this analysis we conclude that the two curves obtained for DLA and DBM (η=1) cannot be distinguished if one takes into account the error bars. This means that finite size effects in the fractal analysis of DLA and DBM (η=1) are quite the same (despite the differences in the algorithms respectively used to generate the electrical trees). To our knowledge no comparison has ever been made between the similarities and differences of the DBM and DLA approach on a geometry other than the open-planar geometry. © 2002 Elsevier Science Ltd. All rights reserved.
title Dielectric breakdown in solids modeled by DBM and DLA
title_short Dielectric breakdown in solids modeled by DBM and DLA
title_full Dielectric breakdown in solids modeled by DBM and DLA
title_fullStr Dielectric breakdown in solids modeled by DBM and DLA
title_full_unstemmed Dielectric breakdown in solids modeled by DBM and DLA
title_sort dielectric breakdown in solids modeled by dbm and dla
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v13_n6_p1333_Irurzun
http://hdl.handle.net/20.500.12110/paper_09600779_v13_n6_p1333_Irurzun
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