On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations
| Main Author: | |
|---|---|
| Publication Date: | 1996 |
| Format: | Article |
| Language: | eng |
| Source: | Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| Download full: | http://hdl.handle.net/10400.2/1470 |
Summary: | 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 $q =\gcd \{j: c_{j}(0)>0\}.$ |
| id |
RCAP_a6dfad3850f36e4da4cdd880085eab1e |
|---|---|
| oai_identifier_str |
oai:repositorioaberto.uab.pt:10400.2/1470 |
| network_acronym_str |
RCAP |
| network_name_str |
Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| repository_id_str |
https://opendoar.ac.uk/repository/7160 |
| spelling |
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/10400.2/1470eng0013-0915 (Print)1464-3839 (Online)info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-26T10:02:05Zoai:repositorioaberto.uab.pt:10400.2/1470Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T21:16:07.028997Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse |
| 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 |
0013-0915 (Print) 1464-3839 (Online) |
| 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia instacron:RCAAP |
| instname_str |
FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia |
| instacron_str |
RCAAP |
| institution |
RCAAP |
| reponame_str |
Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| collection |
Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| repository.name.fl_str_mv |
Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia |
| repository.mail.fl_str_mv |
info@rcaap.pt |
| _version_ |
1833599181910966272 |