A hierarchical cluster system based on Horton-Strahler rules for river networks
Autor(a) principal: | |
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Data de Publicação: | 2002 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/1534 |
Resumo: | We consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river numbers |
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7160 |
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A hierarchical cluster system based on Horton-Strahler rules for river networksCoagulation equationsCluster dynamicsHorton-Strahler rulesWe consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river numbersMassachusetts Institute of TechnologyRepositório AbertoCosta, Fernando Pestana daGrinfeld, MichaelWattis, Jonathan AD2010-07-15T13:42:13Z2002-102002-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1534engCosta, Fernnado Pestana da; Grinfeld, Michael; Wattis, Jonathan A. D. - A hierarchical cluster system based on Horton-Strahler rules for river networks." Studies in Applied Mathematics" [Em linha]. ISSN 1467-9590. Vol.109, nº 3, (October 2002), p. 163-2041467-9590info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:14:15Zoai:repositorioaberto.uab.pt:10400.2/1534Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:20.970289Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
title |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
spellingShingle |
A hierarchical cluster system based on Horton-Strahler rules for river networks Costa, Fernando Pestana da Coagulation equations Cluster dynamics Horton-Strahler rules |
title_short |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
title_full |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
title_fullStr |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
title_full_unstemmed |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
title_sort |
A hierarchical cluster system based on Horton-Strahler rules for river networks |
author |
Costa, Fernando Pestana da |
author_facet |
Costa, Fernando Pestana da Grinfeld, Michael Wattis, Jonathan AD |
author_role |
author |
author2 |
Grinfeld, Michael Wattis, Jonathan AD |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Costa, Fernando Pestana da Grinfeld, Michael Wattis, Jonathan AD |
dc.subject.por.fl_str_mv |
Coagulation equations Cluster dynamics Horton-Strahler rules |
topic |
Coagulation equations Cluster dynamics Horton-Strahler rules |
description |
We consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour of solutions as t ! 1 are ob- tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1; where the functional Ni( ) measures the total amount of clusters of a given xed order i: Exact and approximate equations for the time evolution of these functionals are derived. We also present numerical results that sug- gest the existence of self-similar solutions to these approximate equations and discuss its possible relevance for an interpretation of Horton's law of river numbers |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-10 2002-10-01T00:00:00Z 2010-07-15T13:42:13Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.2/1534 |
url |
http://hdl.handle.net/10400.2/1534 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Costa, Fernnado Pestana da; Grinfeld, Michael; Wattis, Jonathan A. D. - A hierarchical cluster system based on Horton-Strahler rules for river networks." Studies in Applied Mathematics" [Em linha]. ISSN 1467-9590. Vol.109, nº 3, (October 2002), p. 163-204 1467-9590 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Massachusetts Institute of Technology |
publisher.none.fl_str_mv |
Massachusetts Institute of Technology |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799134999876730880 |