First-passage times for pattern formation in nonlocal partial differential equations

Autores
Caceres Garcia Faure, Manuel Osvaldo; Fuentes, Miguel Angel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.
Fil: Caceres Garcia Faure, Manuel Osvaldo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fuentes, Miguel Angel. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Universidad San Sebastian; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Stochastic Process
Non Local Interaction
Population Model
Mfpt
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:11336/42141
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/42141
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling First-passage times for pattern formation in nonlocal partial differential equationsCaceres Garcia Faure, Manuel OsvaldoFuentes, Miguel AngelStochastic ProcessNon Local InteractionPopulation ModelMfpthttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.Fil: Caceres Garcia Faure, Manuel Osvaldo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fuentes, Miguel Angel. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Universidad San Sebastian; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Physical Society2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/42141Caceres Garcia Faure, Manuel Osvaldo; Fuentes, Miguel Angel; First-passage times for pattern formation in nonlocal partial differential equations; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 92; 4; 10-2015; 1-141539-3755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042122info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.92.042122info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:51:52Zoai:ri.conicet.gov.ar:11336/42141instacron: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 09:51:52.566CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv First-passage times for pattern formation in nonlocal partial differential equations
title First-passage times for pattern formation in nonlocal partial differential equations
spellingShingle First-passage times for pattern formation in nonlocal partial differential equations
Caceres Garcia Faure, Manuel Osvaldo
Stochastic Process
Non Local Interaction
Population Model
Mfpt
title_short First-passage times for pattern formation in nonlocal partial differential equations
title_full First-passage times for pattern formation in nonlocal partial differential equations
title_fullStr First-passage times for pattern formation in nonlocal partial differential equations
title_full_unstemmed First-passage times for pattern formation in nonlocal partial differential equations
title_sort First-passage times for pattern formation in nonlocal partial differential equations
dc.creator.none.fl_str_mv Caceres Garcia Faure, Manuel Osvaldo
Fuentes, Miguel Angel
author Caceres Garcia Faure, Manuel Osvaldo
author_facet Caceres Garcia Faure, Manuel Osvaldo
Fuentes, Miguel Angel
author_role author
author2 Fuentes, Miguel Angel
author2_role author
dc.subject.none.fl_str_mv Stochastic Process
Non Local Interaction
Population Model
Mfpt
topic Stochastic Process
Non Local Interaction
Population Model
Mfpt
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.
Fil: Caceres Garcia Faure, Manuel Osvaldo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Fuentes, Miguel Angel. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Universidad San Sebastian; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added to the evolution equation to define the lifetimes and to calculate the mean first-passage time of the stochastic field through a given threshold value, before the patterned steady state is reached. In order to obtain analytical results we introduce a stochastic multiscale perturbation expansion. This multiscale expansion can also be used to tackle multiplicative stochastic partial differential equations. A critical slowing down is predicted for the marginal case when the Fourier phase of the unstable initial condition is null. We carry out Monte Carlo simulations to show the agreement with our theoretical predictions. Analytic results for the bifurcation point and asymptotic analysis of traveling wave-front solutions are included to get insight into the noise-induced transition phenomena mediated by invading fronts.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/42141
Caceres Garcia Faure, Manuel Osvaldo; Fuentes, Miguel Angel; First-passage times for pattern formation in nonlocal partial differential equations; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 92; 4; 10-2015; 1-14
1539-3755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/42141
identifier_str_mv Caceres Garcia Faure, Manuel Osvaldo; Fuentes, Miguel Angel; First-passage times for pattern formation in nonlocal partial differential equations; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 92; 4; 10-2015; 1-14
1539-3755
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://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042122
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.92.042122
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
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
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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