A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy

A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier–Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series, we employ a least-squares fitting to obtain the coefficients...

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Detalhes bibliográficos
Autores: Soulé, Ezequiel Rodolfo, Rey, Alejandro D.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/9754
Acesso em linha:http://hdl.handle.net/11336/9754
Access Level:acceso abierto
Palavra-chave:Liquid Crystal
Phase Transition
Maier–Saupe Theory
Landau–De Gennes Theory
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
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spelling A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energySoulé, Ezequiel RodolfoRey, Alejandro D.Liquid CrystalPhase TransitionMaier–Saupe TheoryLandau–De Gennes Theoryhttps://purl.org/becyt/ford/2.5https://purl.org/becyt/ford/2A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier–Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series, we employ a least-squares fitting to obtain the coefficients of a polynomial expression. Both methods are compared, and the fitting with at most five polynomial terms is shown to provide a satisfactory fitting, and to give much more accurate results than the traditional Taylor expansion. We perform the analysis in terms of the tensor order parameter, so the results are valid in uniaxial and biaxial states.Fil: Soulé, Ezequiel Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigación en Ciencia y Tecnología de Materiales (i); Argentina. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; ArgentinaFil: Rey, Alejandro D.. McGill University; CanadáTaylor & Francis Ltd2011-02-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/9754Soulé, Ezequiel Rodolfo; Rey, Alejandro D.; A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy; Taylor & Francis Ltd; Liquid Crystals; 38; 2; 16-2-2011; 201-2050267-8292enginfo:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/02678292.2010.539303info:eu-repo/semantics/altIdentifier/doi/10.1080/02678292.2010.539303info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:41:37Zoai:ri.conicet.gov.ar:11336/9754instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 13:41:37.717CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
title A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
spellingShingle A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
Soulé, Ezequiel Rodolfo
Liquid Crystal
Phase Transition
Maier–Saupe Theory
Landau–De Gennes Theory
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
title_short A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
title_full A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
title_fullStr A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
title_full_unstemmed A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
title_sort A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy
dc.creator.none.fl_str_mv Soulé, Ezequiel Rodolfo
Rey, Alejandro D.
author Soulé, Ezequiel Rodolfo
author_facet Soulé, Ezequiel Rodolfo
Rey, Alejandro D.
author_role author
author2 Rey, Alejandro D.
author2_role author
dc.subject.none.fl_str_mv Liquid Crystal
Phase Transition
Maier–Saupe Theory
Landau–De Gennes Theory
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
topic Liquid Crystal
Phase Transition
Maier–Saupe Theory
Landau–De Gennes Theory
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
description A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier–Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series, we employ a least-squares fitting to obtain the coefficients of a polynomial expression. Both methods are compared, and the fitting with at most five polynomial terms is shown to provide a satisfactory fitting, and to give much more accurate results than the traditional Taylor expansion. We perform the analysis in terms of the tensor order parameter, so the results are valid in uniaxial and biaxial states.
publishDate 2011
dc.date.none.fl_str_mv 2011-02-16
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/9754
Soulé, Ezequiel Rodolfo; Rey, Alejandro D.; A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy; Taylor & Francis Ltd; Liquid Crystals; 38; 2; 16-2-2011; 201-205
0267-8292
url http://hdl.handle.net/11336/9754
identifier_str_mv Soulé, Ezequiel Rodolfo; Rey, Alejandro D.; A good and computationally efficient polynomial approximation to the Maier–Saupe nematic free energy; Taylor & Francis Ltd; Liquid Crystals; 38; 2; 16-2-2011; 201-205
0267-8292
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/02678292.2010.539303
info:eu-repo/semantics/altIdentifier/doi/10.1080/02678292.2010.539303
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1799195022735704064
score 15,812455

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