Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk

In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a...

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Detalles Bibliográficos
Autores: Sposini, V., Vitali, S., Paradisi, P., Pagnini, G.
Tipo de recurso: capítulo de libro
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1333
Acceso en línea:http://hdl.handle.net/20.500.11824/1333
Access Level:acceso abierto
Palabra clave:Continuos time random walk
medium heterogeneity
anomalous diffusion
time-fractional diffusion
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spelling Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random WalkSposini, V.Vitali, S.Paradisi, P.Pagnini, G.Continuos time random walkmedium heterogeneityanomalous diffusiontime-fractional diffusionIn this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a different time-scale for an exponential survival probability. The resulting process is a non-Markovian non-Gaussian random walk. In particular, for a power-law distribution of the time-scales, the resulting random walk corresponds to a time-fractional diffusion process. We relates the power-law of the medium heterogeneity to the fractional order of the diffusion. This relation provides an interpretation and an estimation of the fractional order of derivation in terms of environment heterogeneity. The results are supported by simulations.202120212021info:eu-repo/semantics/bookPartinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1333reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)InglésReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/13332026-06-19T12:47:47Z
dc.title.none.fl_str_mv Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
title Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
spellingShingle Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
Sposini, V.
Continuos time random walk
medium heterogeneity
anomalous diffusion
time-fractional diffusion
title_short Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
title_full Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
title_fullStr Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
title_full_unstemmed Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
title_sort Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
dc.creator.none.fl_str_mv Sposini, V.
Vitali, S.
Paradisi, P.
Pagnini, G.
author Sposini, V.
author_facet Sposini, V.
Vitali, S.
Paradisi, P.
Pagnini, G.
author_role author
author2 Vitali, S.
Paradisi, P.
Pagnini, G.
author2_role author
author
author
dc.subject.none.fl_str_mv Continuos time random walk
medium heterogeneity
anomalous diffusion
time-fractional diffusion
topic Continuos time random walk
medium heterogeneity
anomalous diffusion
time-fractional diffusion
description In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a different time-scale for an exponential survival probability. The resulting process is a non-Markovian non-Gaussian random walk. In particular, for a power-law distribution of the time-scales, the resulting random walk corresponds to a time-fractional diffusion process. We relates the power-law of the medium heterogeneity to the fractional order of the diffusion. This relation provides an interpretation and an estimation of the fractional order of derivation in terms of environment heterogeneity. The results are supported by simulations.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
info:eu-repo/semantics/acceptedVersion
format bookPart
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1333
url http://hdl.handle.net/20.500.11824/1333
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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collection BIRD. BCAM's Institutional Repository Data
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