KPZ models: Height gradient fluctuations and the tilt method

Autores
Torres, M. F.; Buceta, Ruben Carlos
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
When an interface model belonging to the KPZ universality class is tilted with average slope m, its average velocity increases in Λ/2 m2. The coefficient Λ can only be related to the non-linear coefficient λ from the KPZ equation if the mean square of the height gradient also increases in bm2 when the interface is tilted. For the continuous KPZ equation, b = 1 and the relation Λ = λ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of b. We show that, for one-dimensional discrete KPZ models, 1-b ∼ sγb, where s is the discretization step chosen to calculate the height gradient. The exponent γb that we measure matches the power-law exponent associated with the finite-size corrections of the interface average velocity, i.e. γb = 2(ζ- 1), where ζ is the global roughness exponent. Lastly, we show how, for restricted (unrestricted) growth models, the value of b goes to 1 from below (above) as s increases.
Fil: Torres, M. F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina
Fil: Buceta, Ruben Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina
Materia
CLASSICAL MONTE CARLO SIMULATIONS
GROWTH PROCESSES
INTERFACES IN RANDOM MEDIA
KINETIC ROUGHENING
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/182286
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling KPZ models: Height gradient fluctuations and the tilt methodTorres, M. F.Buceta, Ruben CarlosCLASSICAL MONTE CARLO SIMULATIONSGROWTH PROCESSESINTERFACES IN RANDOM MEDIAKINETIC ROUGHENINGhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1When an interface model belonging to the KPZ universality class is tilted with average slope m, its average velocity increases in Λ/2 m2. The coefficient Λ can only be related to the non-linear coefficient λ from the KPZ equation if the mean square of the height gradient also increases in bm2 when the interface is tilted. For the continuous KPZ equation, b = 1 and the relation Λ = λ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of b. We show that, for one-dimensional discrete KPZ models, 1-b ∼ sγb, where s is the discretization step chosen to calculate the height gradient. The exponent γb that we measure matches the power-law exponent associated with the finite-size corrections of the interface average velocity, i.e. γb = 2(ζ- 1), where ζ is the global roughness exponent. Lastly, we show how, for restricted (unrestricted) growth models, the value of b goes to 1 from below (above) as s increases.Fil: Torres, M. F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Buceta, Ruben Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaIOP Publishing2021-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/182286Torres, M. F.; Buceta, Ruben Carlos; KPZ models: Height gradient fluctuations and the tilt method; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2021; 9; 9-2021; 1-91742-5468CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1742-5468/ac1f10info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/ac1f10info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.09652info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:27:10Zoai:ri.conicet.gov.ar:11336/182286instacron: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:34982025-09-29 10:27:10.35CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv KPZ models: Height gradient fluctuations and the tilt method
title KPZ models: Height gradient fluctuations and the tilt method
spellingShingle KPZ models: Height gradient fluctuations and the tilt method
Torres, M. F.
CLASSICAL MONTE CARLO SIMULATIONS
GROWTH PROCESSES
INTERFACES IN RANDOM MEDIA
KINETIC ROUGHENING
title_short KPZ models: Height gradient fluctuations and the tilt method
title_full KPZ models: Height gradient fluctuations and the tilt method
title_fullStr KPZ models: Height gradient fluctuations and the tilt method
title_full_unstemmed KPZ models: Height gradient fluctuations and the tilt method
title_sort KPZ models: Height gradient fluctuations and the tilt method
dc.creator.none.fl_str_mv Torres, M. F.
Buceta, Ruben Carlos
author Torres, M. F.
author_facet Torres, M. F.
Buceta, Ruben Carlos
author_role author
author2 Buceta, Ruben Carlos
author2_role author
dc.subject.none.fl_str_mv CLASSICAL MONTE CARLO SIMULATIONS
GROWTH PROCESSES
INTERFACES IN RANDOM MEDIA
KINETIC ROUGHENING
topic CLASSICAL MONTE CARLO SIMULATIONS
GROWTH PROCESSES
INTERFACES IN RANDOM MEDIA
KINETIC ROUGHENING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv When an interface model belonging to the KPZ universality class is tilted with average slope m, its average velocity increases in Λ/2 m2. The coefficient Λ can only be related to the non-linear coefficient λ from the KPZ equation if the mean square of the height gradient also increases in bm2 when the interface is tilted. For the continuous KPZ equation, b = 1 and the relation Λ = λ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of b. We show that, for one-dimensional discrete KPZ models, 1-b ∼ sγb, where s is the discretization step chosen to calculate the height gradient. The exponent γb that we measure matches the power-law exponent associated with the finite-size corrections of the interface average velocity, i.e. γb = 2(ζ- 1), where ζ is the global roughness exponent. Lastly, we show how, for restricted (unrestricted) growth models, the value of b goes to 1 from below (above) as s increases.
Fil: Torres, M. F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina
Fil: Buceta, Ruben Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina
description When an interface model belonging to the KPZ universality class is tilted with average slope m, its average velocity increases in Λ/2 m2. The coefficient Λ can only be related to the non-linear coefficient λ from the KPZ equation if the mean square of the height gradient also increases in bm2 when the interface is tilted. For the continuous KPZ equation, b = 1 and the relation Λ = λ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of b. We show that, for one-dimensional discrete KPZ models, 1-b ∼ sγb, where s is the discretization step chosen to calculate the height gradient. The exponent γb that we measure matches the power-law exponent associated with the finite-size corrections of the interface average velocity, i.e. γb = 2(ζ- 1), where ζ is the global roughness exponent. Lastly, we show how, for restricted (unrestricted) growth models, the value of b goes to 1 from below (above) as s increases.
publishDate 2021
dc.date.none.fl_str_mv 2021-09
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/11336/182286
Torres, M. F.; Buceta, Ruben Carlos; KPZ models: Height gradient fluctuations and the tilt method; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2021; 9; 9-2021; 1-9
1742-5468
CONICET Digital
CONICET
url http://hdl.handle.net/11336/182286
identifier_str_mv Torres, M. F.; Buceta, Ruben Carlos; KPZ models: Height gradient fluctuations and the tilt method; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2021; 9; 9-2021; 1-9
1742-5468
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1742-5468/ac1f10
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/ac1f10
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.09652
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 IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
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
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score 13.070432

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