Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus

The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy production, and using the time fractional derivativ...

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Autores: Garcia-Bernabé, Abel, Hernández, Saul Iván, del Castillo, L. F., Jou i Mirabent, David|||0000-0003-3731-5877
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:170161
Acceso en línea:https://ddd.uab.cat/record/170161
https://dx.doi.org/urn:doi:10.3390/math4040067
Access Level:acceso abierto
Palabra clave:Transport phenomena
Anomalous transport
Continued fraction
Extended Irreversible
Thermodynamics
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spelling Continued-Fraction Expansion of Transport Coefficients with Fractional CalculusGarcia-Bernabé, AbelHernández, Saul Ivándel Castillo, L. F.Jou i Mirabent, David|||0000-0003-3731-5877Transport phenomenaAnomalous transportContinued fractionExtended IrreversibleThermodynamicsThe main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy production, and using the time fractional derivative, we have derived a space-time generalized telegrapher's equation with a fractional nested hierarchy which can be used in separate developments for the mass transport, for the heat conduction and for the flux of ions. We have obtained a new formalism which includes the contribution of fast of higher-order fluxes in the mesoscopic and inhomogeneous media. The results take the form of continued fraction expansions. The balance equations are used in a scheme of continued fractions, and they appear as a closure condition. In this way the transport equation and its corresponding wave number-frequency relation are obtained, both of them in the mathematical structure of the continued fraction scheme. Numerical examples are included to show the dispersive nature of the solutions, and the generalized fractional transport equation in the same mathematical form, which can be applied to the mass transport, the heat conduction and the flux of ions. 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/170161https://dx.doi.org/urn:doi:10.3390/math4040067reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1701612026-06-06T12:50:31Z
dc.title.none.fl_str_mv Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
title Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
spellingShingle Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
Garcia-Bernabé, Abel
Transport phenomena
Anomalous transport
Continued fraction
Extended Irreversible
Thermodynamics
title_short Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
title_full Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
title_fullStr Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
title_full_unstemmed Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
title_sort Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
dc.creator.none.fl_str_mv Garcia-Bernabé, Abel
Hernández, Saul Iván
del Castillo, L. F.
Jou i Mirabent, David|||0000-0003-3731-5877
author Garcia-Bernabé, Abel
author_facet Garcia-Bernabé, Abel
Hernández, Saul Iván
del Castillo, L. F.
Jou i Mirabent, David|||0000-0003-3731-5877
author_role author
author2 Hernández, Saul Iván
del Castillo, L. F.
Jou i Mirabent, David|||0000-0003-3731-5877
author2_role author
author
author
dc.subject.none.fl_str_mv Transport phenomena
Anomalous transport
Continued fraction
Extended Irreversible
Thermodynamics
topic Transport phenomena
Anomalous transport
Continued fraction
Extended Irreversible
Thermodynamics
description The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy production, and using the time fractional derivative, we have derived a space-time generalized telegrapher's equation with a fractional nested hierarchy which can be used in separate developments for the mass transport, for the heat conduction and for the flux of ions. We have obtained a new formalism which includes the contribution of fast of higher-order fluxes in the mesoscopic and inhomogeneous media. The results take the form of continued fraction expansions. The balance equations are used in a scheme of continued fractions, and they appear as a closure condition. In this way the transport equation and its corresponding wave number-frequency relation are obtained, both of them in the mathematical structure of the continued fraction scheme. Numerical examples are included to show the dispersive nature of the solutions, and the generalized fractional transport equation in the same mathematical form, which can be applied to the mass transport, the heat conduction and the flux of ions.
publishDate 2016
dc.date.none.fl_str_mv 2
2016-01-01
2016
2016-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/170161
https://dx.doi.org/urn:doi:10.3390/math4040067
url https://ddd.uab.cat/record/170161
https://dx.doi.org/urn:doi:10.3390/math4040067
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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