Self-similar resistive circuits as fractal-like structures

Detalhes bibliográficos
Autor(a) principal: Santos,Claudio Xavier Mendes dos
Data de Publicação: 2018
Outros Autores: Mendes,Carlos Molina, Freire,Marcelo Ventura
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100402
Resumo: Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.
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spelling Self-similar resistive circuits as fractal-like structuresself-similarityresistive circuitfractalFractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.Sociedade Brasileira de Física2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100402Revista Brasileira de Ensino de Física v.40 n.1 2018reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2017-0178info:eu-repo/semantics/openAccessSantos,Claudio Xavier Mendes dosMendes,Carlos MolinaFreire,Marcelo Venturaeng2017-09-29T00:00:00Zoai:scielo:S1806-11172018000100402Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2017-09-29T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Self-similar resistive circuits as fractal-like structures
title Self-similar resistive circuits as fractal-like structures
spellingShingle Self-similar resistive circuits as fractal-like structures
Santos,Claudio Xavier Mendes dos
self-similarity
resistive circuit
fractal
title_short Self-similar resistive circuits as fractal-like structures
title_full Self-similar resistive circuits as fractal-like structures
title_fullStr Self-similar resistive circuits as fractal-like structures
title_full_unstemmed Self-similar resistive circuits as fractal-like structures
title_sort Self-similar resistive circuits as fractal-like structures
author Santos,Claudio Xavier Mendes dos
author_facet Santos,Claudio Xavier Mendes dos
Mendes,Carlos Molina
Freire,Marcelo Ventura
author_role author
author2 Mendes,Carlos Molina
Freire,Marcelo Ventura
author2_role author
author
dc.contributor.author.fl_str_mv Santos,Claudio Xavier Mendes dos
Mendes,Carlos Molina
Freire,Marcelo Ventura
dc.subject.por.fl_str_mv self-similarity
resistive circuit
fractal
topic self-similarity
resistive circuit
fractal
description Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100402
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100402
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2017-0178
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.40 n.1 2018
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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