The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective

Autores
Wio, Horacio S.; Deza, Roberto Raul; Revelli, Jorge Alberto; Gallego, Rafael; García García, Reinaldo; Rodríguez, Miguel A.
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, orsemiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affinefractals, and feature scaling with universal exponents (depending on the substrate’s dimensionalityd and global topology, as well as on the driving randomness’ spatial andtemporal correlations but not on the underlying mechanisms). Adding lateral growth asan essential (non-equilibrium) ingredient to the known equilibrium ones (randomnessand interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding(via the dynamic renormalization group) the correct exponents for flat d = 1 substratesand (spatially and temporally) uncorrelated randomness. It is this interplay which givesrise to the unique, non-Gaussian scaling properties characteristic of the specific, universaltype of non-equilibrium roughening. Later on, the asymptotic statistics of process h(x)fluctuations in the scaling regime was also analytically found for d = 1 substrates. Ford > 1 substrates, however, one has to rely on numerical simulations. Here we reviewa variational approach that allows for analytical progress regardless of substrate dimensionality.After reviewing our previous numerical results in d = 1, 2, and 3 on the timeevolution of one of the functionals—which we call the non-equilibrium potential (NEP)—aswell as its scaling behavior with the nonlinearity parameter λ, we discuss the stochasticthermodynamics of the roughening process and the memory of process h(x) in KPZ andin the related Golubovi´c–Bruinsma (GB) model, providing numerical evidence for thesignificant dependence on initial conditions of the NEP’s asymptotic behavior in bothmodels. Finally, we highlight some open questions.
Fil: Wio, Horacio S.. Consejo Superior de Investigaciones Científicas; España
Fil: Deza, Roberto Raul. 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
Fil: Revelli, Jorge Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Gallego, Rafael. Universidad de Oviedo; España
Fil: García García, Reinaldo. Universidad de Navarra; España
Fil: Rodríguez, Miguel A.. Universidad de Cantabria; España
Materia
KINETICS
INTERFACE
ROUGHENING
VARIATIONAL
APPROACH
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/289565
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The KPZ Equation of Kinetic Interface Roughening: A Variational PerspectiveWio, Horacio S.Deza, Roberto RaulRevelli, Jorge AlbertoGallego, RafaelGarcía García, ReinaldoRodríguez, Miguel A.KINETICSINTERFACEROUGHENINGVARIATIONALAPPROACHhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, orsemiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affinefractals, and feature scaling with universal exponents (depending on the substrate’s dimensionalityd and global topology, as well as on the driving randomness’ spatial andtemporal correlations but not on the underlying mechanisms). Adding lateral growth asan essential (non-equilibrium) ingredient to the known equilibrium ones (randomnessand interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding(via the dynamic renormalization group) the correct exponents for flat d = 1 substratesand (spatially and temporally) uncorrelated randomness. It is this interplay which givesrise to the unique, non-Gaussian scaling properties characteristic of the specific, universaltype of non-equilibrium roughening. Later on, the asymptotic statistics of process h(x)fluctuations in the scaling regime was also analytically found for d = 1 substrates. Ford > 1 substrates, however, one has to rely on numerical simulations. Here we reviewa variational approach that allows for analytical progress regardless of substrate dimensionality.After reviewing our previous numerical results in d = 1, 2, and 3 on the timeevolution of one of the functionals—which we call the non-equilibrium potential (NEP)—aswell as its scaling behavior with the nonlinearity parameter λ, we discuss the stochasticthermodynamics of the roughening process and the memory of process h(x) in KPZ andin the related Golubovi´c–Bruinsma (GB) model, providing numerical evidence for thesignificant dependence on initial conditions of the NEP’s asymptotic behavior in bothmodels. Finally, we highlight some open questions.Fil: Wio, Horacio S.. Consejo Superior de Investigaciones Científicas; EspañaFil: Deza, Roberto Raul. 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; ArgentinaFil: Revelli, Jorge Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Gallego, Rafael. Universidad de Oviedo; EspañaFil: García García, Reinaldo. Universidad de Navarra; EspañaFil: Rodríguez, Miguel A.. Universidad de Cantabria; EspañaMolecular Diversity Preservation International2025-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/289565Wio, Horacio S.; Deza, Roberto Raul; Revelli, Jorge Alberto; Gallego, Rafael; García García, Reinaldo; et al.; The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective; Molecular Diversity Preservation International; Entropy; 28; 1; 12-2025; 1-171099-4300CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/28/1/55info:eu-repo/semantics/altIdentifier/doi/10.3390/e28010055info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T14:32:05Zoai:ri.conicet.gov.ar:11336/289565instacron: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:34982026-08-25 14:32:05.69CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
title The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
spellingShingle The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
Wio, Horacio S.
KINETICS
INTERFACE
ROUGHENING
VARIATIONAL
APPROACH
title_short The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
title_full The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
title_fullStr The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
title_full_unstemmed The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
title_sort The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
dc.creator.none.fl_str_mv Wio, Horacio S.
Deza, Roberto Raul
Revelli, Jorge Alberto
Gallego, Rafael
García García, Reinaldo
Rodríguez, Miguel A.
author Wio, Horacio S.
author_facet Wio, Horacio S.
Deza, Roberto Raul
Revelli, Jorge Alberto
Gallego, Rafael
García García, Reinaldo
Rodríguez, Miguel A.
author_role author
author2 Deza, Roberto Raul
Revelli, Jorge Alberto
Gallego, Rafael
García García, Reinaldo
Rodríguez, Miguel A.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv KINETICS
INTERFACE
ROUGHENING
VARIATIONAL
APPROACH
topic KINETICS
INTERFACE
ROUGHENING
VARIATIONAL
APPROACH
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, orsemiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affinefractals, and feature scaling with universal exponents (depending on the substrate’s dimensionalityd and global topology, as well as on the driving randomness’ spatial andtemporal correlations but not on the underlying mechanisms). Adding lateral growth asan essential (non-equilibrium) ingredient to the known equilibrium ones (randomnessand interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding(via the dynamic renormalization group) the correct exponents for flat d = 1 substratesand (spatially and temporally) uncorrelated randomness. It is this interplay which givesrise to the unique, non-Gaussian scaling properties characteristic of the specific, universaltype of non-equilibrium roughening. Later on, the asymptotic statistics of process h(x)fluctuations in the scaling regime was also analytically found for d = 1 substrates. Ford > 1 substrates, however, one has to rely on numerical simulations. Here we reviewa variational approach that allows for analytical progress regardless of substrate dimensionality.After reviewing our previous numerical results in d = 1, 2, and 3 on the timeevolution of one of the functionals—which we call the non-equilibrium potential (NEP)—aswell as its scaling behavior with the nonlinearity parameter λ, we discuss the stochasticthermodynamics of the roughening process and the memory of process h(x) in KPZ andin the related Golubovi´c–Bruinsma (GB) model, providing numerical evidence for thesignificant dependence on initial conditions of the NEP’s asymptotic behavior in bothmodels. Finally, we highlight some open questions.
Fil: Wio, Horacio S.. Consejo Superior de Investigaciones Científicas; España
Fil: Deza, Roberto Raul. 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
Fil: Revelli, Jorge Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Gallego, Rafael. Universidad de Oviedo; España
Fil: García García, Reinaldo. Universidad de Navarra; España
Fil: Rodríguez, Miguel A.. Universidad de Cantabria; España
description Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, orsemiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affinefractals, and feature scaling with universal exponents (depending on the substrate’s dimensionalityd and global topology, as well as on the driving randomness’ spatial andtemporal correlations but not on the underlying mechanisms). Adding lateral growth asan essential (non-equilibrium) ingredient to the known equilibrium ones (randomnessand interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding(via the dynamic renormalization group) the correct exponents for flat d = 1 substratesand (spatially and temporally) uncorrelated randomness. It is this interplay which givesrise to the unique, non-Gaussian scaling properties characteristic of the specific, universaltype of non-equilibrium roughening. Later on, the asymptotic statistics of process h(x)fluctuations in the scaling regime was also analytically found for d = 1 substrates. Ford > 1 substrates, however, one has to rely on numerical simulations. Here we reviewa variational approach that allows for analytical progress regardless of substrate dimensionality.After reviewing our previous numerical results in d = 1, 2, and 3 on the timeevolution of one of the functionals—which we call the non-equilibrium potential (NEP)—aswell as its scaling behavior with the nonlinearity parameter λ, we discuss the stochasticthermodynamics of the roughening process and the memory of process h(x) in KPZ andin the related Golubovi´c–Bruinsma (GB) model, providing numerical evidence for thesignificant dependence on initial conditions of the NEP’s asymptotic behavior in bothmodels. Finally, we highlight some open questions.
publishDate 2025
dc.date.none.fl_str_mv 2025-12
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/11336/289565
Wio, Horacio S.; Deza, Roberto Raul; Revelli, Jorge Alberto; Gallego, Rafael; García García, Reinaldo; et al.; The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective; Molecular Diversity Preservation International; Entropy; 28; 1; 12-2025; 1-17
1099-4300
CONICET Digital
CONICET
url http://hdl.handle.net/11336/289565
identifier_str_mv Wio, Horacio S.; Deza, Roberto Raul; Revelli, Jorge Alberto; Gallego, Rafael; García García, Reinaldo; et al.; The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective; Molecular Diversity Preservation International; Entropy; 28; 1; 12-2025; 1-17
1099-4300
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://www.mdpi.com/1099-4300/28/1/55
info:eu-repo/semantics/altIdentifier/doi/10.3390/e28010055
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Molecular Diversity Preservation International
publisher.none.fl_str_mv Molecular Diversity Preservation International
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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