On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations
Autor(a) principal: | |
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Data de Publicação: | 1996 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/1470 |
Resumo: | In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations $$\dot{c}_{j} = \sum_{k=1}^{j-1}c_{j-k}c_{k} - 2c_{j}\sum_{k=1}^{\infty}c_{k}, j = 1, 2, \ldots$$ with general exponentially decreasing initial data, with density $\rho,$ have the following asymptotic behaviour $$\lim_{j, t \rightarrow\infty, \xi = j/t fixed, j \in {\cal J}} t^{2}c_{j}(t) = \frac{q}{\rho}\, e^{-\xi/\rho},$$ where ${\cal J} = \{j: c_{j}(t)>0, t>0\}$ and $q =\gcd \{j: c_{j}(0)>0\}.$ |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equationsSmoluchowski coagulation equationsSelf-similar solutionsIn this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations $$\dot{c}_{j} = \sum_{k=1}^{j-1}c_{j-k}c_{k} - 2c_{j}\sum_{k=1}^{\infty}c_{k}, j = 1, 2, \ldots$$ with general exponentially decreasing initial data, with density $\rho,$ have the following asymptotic behaviour $$\lim_{j, t \rightarrow\infty, \xi = j/t fixed, j \in {\cal J}} t^{2}c_{j}(t) = \frac{q}{\rho}\, e^{-\xi/\rho},$$ where ${\cal J} = \{j: c_{j}(t)>0, t>0\}$ and $q =\gcd \{j: c_{j}(0)>0\}.$Cambridge University PressRepositório AbertoCosta, Fernando Pestana da2010-05-14T13:52:24Z19961996-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1470engCosta, Fernando Pestana da - On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations. "Proceedings of the Edinburgh Mathematical Society" [Em linha]. ISSN 0013-0915 (Print)1464-3839 (Online). Nº 39 (1996), p. 547-5590013-0915 (Print)info: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:RCAAP2023-07-07T15:59:11ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
title |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
spellingShingle |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations Costa, Fernando Pestana da Smoluchowski coagulation equations Self-similar solutions |
title_short |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
title_full |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
title_fullStr |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
title_full_unstemmed |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
title_sort |
On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations |
author |
Costa, Fernando Pestana da |
author_facet |
Costa, Fernando Pestana da |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Costa, Fernando Pestana da |
dc.subject.por.fl_str_mv |
Smoluchowski coagulation equations Self-similar solutions |
topic |
Smoluchowski coagulation equations Self-similar solutions |
description |
In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations $$\dot{c}_{j} = \sum_{k=1}^{j-1}c_{j-k}c_{k} - 2c_{j}\sum_{k=1}^{\infty}c_{k}, j = 1, 2, \ldots$$ with general exponentially decreasing initial data, with density $\rho,$ have the following asymptotic behaviour $$\lim_{j, t \rightarrow\infty, \xi = j/t fixed, j \in {\cal J}} t^{2}c_{j}(t) = \frac{q}{\rho}\, e^{-\xi/\rho},$$ where ${\cal J} = \{j: c_{j}(t)>0, t>0\}$ and $q =\gcd \{j: c_{j}(0)>0\}.$ |
publishDate |
1996 |
dc.date.none.fl_str_mv |
1996 1996-01-01T00:00:00Z 2010-05-14T13:52:24Z |
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/10400.2/1470 |
url |
http://hdl.handle.net/10400.2/1470 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Costa, Fernando Pestana da - On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations. "Proceedings of the Edinburgh Mathematical Society" [Em linha]. ISSN 0013-0915 (Print)1464-3839 (Online). Nº 39 (1996), p. 547-559 0013-0915 (Print) |
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 |
Cambridge University Press |
publisher.none.fl_str_mv |
Cambridge University Press |
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) |
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repository.mail.fl_str_mv |
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1777302836817690624 |