Non-Gaussian distributions to random walk in the context of memory kernels
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/195080 |
Resumo: | The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context. |
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Santos, Maike Antonio Faustino dos2019-06-05T02:33:50Z20182504-3110http://hdl.handle.net/10183/195080001091964The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context.application/pdfengFractal and fractional. Basel. Vol. 2, no. 3 (Sept. 2018), 20, 15 p.Física estatísticaProbabilidadeProcessos estocásticosFractional diffusion equationMemory kernelsRandom walkDiffusion modelsSolution techniquesAnomalous diffusionNon-Gaussian distributions to random walk in the context of memory kernelsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001091964.pdf.txt001091964.pdf.txtExtracted Texttext/plain40727http://www.lume.ufrgs.br/bitstream/10183/195080/2/001091964.pdf.txt3d6d849df8bcc03a302f145121030fc4MD52ORIGINAL001091964.pdfTexto completo (inglês)application/pdf894133http://www.lume.ufrgs.br/bitstream/10183/195080/1/001091964.pdf673c6be13f64f8fca98b9e9e8606d8ddMD5110183/1950802022-02-22 05:07:59.673429oai:www.lume.ufrgs.br:10183/195080Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2022-02-22T08:07:59Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Non-Gaussian distributions to random walk in the context of memory kernels |
title |
Non-Gaussian distributions to random walk in the context of memory kernels |
spellingShingle |
Non-Gaussian distributions to random walk in the context of memory kernels Santos, Maike Antonio Faustino dos Física estatística Probabilidade Processos estocásticos Fractional diffusion equation Memory kernels Random walk Diffusion models Solution techniques Anomalous diffusion |
title_short |
Non-Gaussian distributions to random walk in the context of memory kernels |
title_full |
Non-Gaussian distributions to random walk in the context of memory kernels |
title_fullStr |
Non-Gaussian distributions to random walk in the context of memory kernels |
title_full_unstemmed |
Non-Gaussian distributions to random walk in the context of memory kernels |
title_sort |
Non-Gaussian distributions to random walk in the context of memory kernels |
author |
Santos, Maike Antonio Faustino dos |
author_facet |
Santos, Maike Antonio Faustino dos |
author_role |
author |
dc.contributor.author.fl_str_mv |
Santos, Maike Antonio Faustino dos |
dc.subject.por.fl_str_mv |
Física estatística Probabilidade Processos estocásticos |
topic |
Física estatística Probabilidade Processos estocásticos Fractional diffusion equation Memory kernels Random walk Diffusion models Solution techniques Anomalous diffusion |
dc.subject.eng.fl_str_mv |
Fractional diffusion equation Memory kernels Random walk Diffusion models Solution techniques Anomalous diffusion |
description |
The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018 |
dc.date.accessioned.fl_str_mv |
2019-06-05T02:33:50Z |
dc.type.driver.fl_str_mv |
Estrangeiro 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://hdl.handle.net/10183/195080 |
dc.identifier.issn.pt_BR.fl_str_mv |
2504-3110 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001091964 |
identifier_str_mv |
2504-3110 001091964 |
url |
http://hdl.handle.net/10183/195080 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Fractal and fractional. Basel. Vol. 2, no. 3 (Sept. 2018), 20, 15 p. |
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.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRGS instname:Universidade Federal do Rio Grande do Sul (UFRGS) instacron:UFRGS |
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UFRGS |
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UFRGS |
reponame_str |
Repositório Institucional da UFRGS |
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Repositório Institucional da UFRGS |
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http://www.lume.ufrgs.br/bitstream/10183/195080/2/001091964.pdf.txt http://www.lume.ufrgs.br/bitstream/10183/195080/1/001091964.pdf |
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Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS) |
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