Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The d...

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Detalles Bibliográficos
Autores: Corral, Álvaro, Díaz Guilera, Albert
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1997
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/18804
Acceso en línea:https://hdl.handle.net/2445/18804
Access Level:acceso abierto
Palabra clave:Física estadística
Termodinàmica
Sistemes no lineals
Propietats magnètiques
Equacions d'estat
Regla de les fases i equilibri
Transformacions de fase (Física estadística)
Equacions diferencials estocàstiques
Statistical physics
Thermodynamics
Nonlinear systems
Magnetic properties
Equations of state
Phase rule and equilibrium
Phase transformations (Statistical physics)
Stochastic differential equations
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spelling Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticalityCorral, ÁlvaroDíaz Guilera, AlbertFísica estadísticaTermodinàmicaSistemes no linealsPropietats magnètiquesEquacions d'estatRegla de les fases i equilibriTransformacions de fase (Física estadística)Equacions diferencials estocàstiquesStatistical physicsThermodynamicsNonlinear systemsMagnetic propertiesEquations of statePhase rule and equilibriumPhase transformations (Statistical physics)Stochastic differential equationsA stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.The American Physical Society201120111997info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion12 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/18804Articles publicats en revistes (Física de la Matèria Condensada)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.55.2434Physical Review E, 1997, vol. 55, núm. 3, p. 2434-2445http://dx.doi.org/10.1103/PhysRevE.55.2434(c) American Physical Society, 1997info:eu-repo/semantics/openAccessoai:recercat.cat:2445/188042026-05-29T05:05:01Z
dc.title.none.fl_str_mv Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
title Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
spellingShingle Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
Corral, Álvaro
Física estadística
Termodinàmica
Sistemes no lineals
Propietats magnètiques
Equacions d'estat
Regla de les fases i equilibri
Transformacions de fase (Física estadística)
Equacions diferencials estocàstiques
Statistical physics
Thermodynamics
Nonlinear systems
Magnetic properties
Equations of state
Phase rule and equilibrium
Phase transformations (Statistical physics)
Stochastic differential equations
title_short Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
title_full Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
title_fullStr Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
title_full_unstemmed Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
title_sort Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality
dc.creator.none.fl_str_mv Corral, Álvaro
Díaz Guilera, Albert
author Corral, Álvaro
author_facet Corral, Álvaro
Díaz Guilera, Albert
author_role author
author2 Díaz Guilera, Albert
author2_role author
dc.subject.none.fl_str_mv Física estadística
Termodinàmica
Sistemes no lineals
Propietats magnètiques
Equacions d'estat
Regla de les fases i equilibri
Transformacions de fase (Física estadística)
Equacions diferencials estocàstiques
Statistical physics
Thermodynamics
Nonlinear systems
Magnetic properties
Equations of state
Phase rule and equilibrium
Phase transformations (Statistical physics)
Stochastic differential equations
topic Física estadística
Termodinàmica
Sistemes no lineals
Propietats magnètiques
Equacions d'estat
Regla de les fases i equilibri
Transformacions de fase (Física estadística)
Equacions diferencials estocàstiques
Statistical physics
Thermodynamics
Nonlinear systems
Magnetic properties
Equations of state
Phase rule and equilibrium
Phase transformations (Statistical physics)
Stochastic differential equations
description A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.
publishDate 1997
dc.date.none.fl_str_mv 1997
2011
2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/18804
url https://hdl.handle.net/2445/18804
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.55.2434
Physical Review E, 1997, vol. 55, núm. 3, p. 2434-2445
http://dx.doi.org/10.1103/PhysRevE.55.2434
dc.rights.none.fl_str_mv (c) American Physical Society, 1997
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Physical Society, 1997
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 12 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv The American Physical Society
publisher.none.fl_str_mv The American Physical Society
dc.source.none.fl_str_mv Articles publicats en revistes (Física de la Matèria Condensada)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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