LotaV3, Main, Exploration, bibRecord, 000034

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

Identifieur interne : 000034 ( Main/Exploration ); précédent : 000033; suivant : 000035

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

Auteurs : Manuel O. Cáceres [Argentine] ; Miguel A. Fuentes [États-Unis, Argentine, Chili]

Source :

Physical review. E, Statistical, nonlinear, and soft matter physics [ 1550-2376 ] ; 2015.

RBID : pubmed:26565183

Abstract

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.

DOI: 10.1103/PhysRevE.92.042122
PubMed: 26565183

Affiliations:

Argentine, Chili, États-Unis

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">First-passage times for pattern formation in nonlocal partial differential equations.</title>
<author><name sortKey="Caceres, Manuel O" sort="Caceres, Manuel O" uniqKey="Caceres M" first="Manuel O" last="Cáceres">Manuel O. Cáceres</name>
<affiliation wicri:level="1"><nlm:affiliation>Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, Avenida E. Bustillo 9500, CP 8400, Bariloche, Argentina.</nlm:affiliation>
<country xml:lang="fr">Argentine</country>
<wicri:regionArea>Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, Avenida E. Bustillo 9500, CP 8400, Bariloche</wicri:regionArea>
<wicri:noRegion>Bariloche</wicri:noRegion>
</affiliation>
</author>
<author><name sortKey="Fuentes, Miguel A" sort="Fuentes, Miguel A" uniqKey="Fuentes M" first="Miguel A" last="Fuentes">Miguel A. Fuentes</name>
<affiliation wicri:level="1"><nlm:affiliation>Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.</nlm:affiliation>
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501</wicri:regionArea>
<wicri:noRegion>New Mexico 87501</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><nlm:affiliation>Instituto de Investigaciones Filosóficas, Bulnes 642, Buenos Aires 1428, Argentina.</nlm:affiliation>
<country xml:lang="fr">Argentine</country>
<wicri:regionArea>Instituto de Investigaciones Filosóficas, Bulnes 642, Buenos Aires 1428</wicri:regionArea>
<wicri:noRegion>Buenos Aires 1428</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><nlm:affiliation>Universidad San Sebastián, Lota 2465, Santiago 7500000, Chile.</nlm:affiliation>
<country xml:lang="fr">Chili</country>
<wicri:regionArea>Universidad San Sebastián, Lota 2465, Santiago 7500000</wicri:regionArea>
<wicri:noRegion>Santiago 7500000</wicri:noRegion>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">PubMed</idno>
<date when="2015">2015</date>
<idno type="doi">10.1103/PhysRevE.92.042122</idno>
<idno type="RBID">pubmed:26565183</idno>
<idno type="pmid">26565183</idno>
<idno type="wicri:Area/PubMed/Corpus">000003</idno>
<idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">000003</idno>
<idno type="wicri:Area/PubMed/Curation">000003</idno>
<idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Curation">000003</idno>
<idno type="wicri:Area/PubMed/Checkpoint">000009</idno>
<idno type="wicri:explorRef" wicri:stream="Checkpoint" wicri:step="PubMed">000009</idno>
<idno type="wicri:Area/Ncbi/Merge">000407</idno>
<idno type="wicri:Area/Ncbi/Curation">000407</idno>
<idno type="wicri:Area/Ncbi/Checkpoint">000407</idno>
<idno type="wicri:Area/Main/Merge">000034</idno>
<idno type="wicri:Area/Main/Curation">000034</idno>
<idno type="wicri:Area/Main/Exploration">000034</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">First-passage times for pattern formation in nonlocal partial differential equations.</title>
<author><name sortKey="Caceres, Manuel O" sort="Caceres, Manuel O" uniqKey="Caceres M" first="Manuel O" last="Cáceres">Manuel O. Cáceres</name>
<affiliation wicri:level="1"><nlm:affiliation>Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, Avenida E. Bustillo 9500, CP 8400, Bariloche, Argentina.</nlm:affiliation>
<country xml:lang="fr">Argentine</country>
<wicri:regionArea>Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, Avenida E. Bustillo 9500, CP 8400, Bariloche</wicri:regionArea>
<wicri:noRegion>Bariloche</wicri:noRegion>
</affiliation>
</author>
<author><name sortKey="Fuentes, Miguel A" sort="Fuentes, Miguel A" uniqKey="Fuentes M" first="Miguel A" last="Fuentes">Miguel A. Fuentes</name>
<affiliation wicri:level="1"><nlm:affiliation>Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.</nlm:affiliation>
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501</wicri:regionArea>
<wicri:noRegion>New Mexico 87501</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><nlm:affiliation>Instituto de Investigaciones Filosóficas, Bulnes 642, Buenos Aires 1428, Argentina.</nlm:affiliation>
<country xml:lang="fr">Argentine</country>
<wicri:regionArea>Instituto de Investigaciones Filosóficas, Bulnes 642, Buenos Aires 1428</wicri:regionArea>
<wicri:noRegion>Buenos Aires 1428</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><nlm:affiliation>Universidad San Sebastián, Lota 2465, Santiago 7500000, Chile.</nlm:affiliation>
<country xml:lang="fr">Chili</country>
<wicri:regionArea>Universidad San Sebastián, Lota 2465, Santiago 7500000</wicri:regionArea>
<wicri:noRegion>Santiago 7500000</wicri:noRegion>
</affiliation>
</author>
</analytic>
<series><title level="j">Physical review. E, Statistical, nonlinear, and soft matter physics</title>
<idno type="eISSN">1550-2376</idno>
<imprint><date when="2015" type="published">2015</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">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.</div>
</front>
</TEI>
<affiliations><list><country><li>Argentine</li>
<li>Chili</li>
<li>États-Unis</li>
</country>
</list>
<tree><country name="Argentine"><noRegion><name sortKey="Caceres, Manuel O" sort="Caceres, Manuel O" uniqKey="Caceres M" first="Manuel O" last="Cáceres">Manuel O. Cáceres</name>
</noRegion>
<name sortKey="Fuentes, Miguel A" sort="Fuentes, Miguel A" uniqKey="Fuentes M" first="Miguel A" last="Fuentes">Miguel A. Fuentes</name>
</country>
<country name="États-Unis"><noRegion><name sortKey="Fuentes, Miguel A" sort="Fuentes, Miguel A" uniqKey="Fuentes M" first="Miguel A" last="Fuentes">Miguel A. Fuentes</name>
</noRegion>
</country>
<country name="Chili"><noRegion><name sortKey="Fuentes, Miguel A" sort="Fuentes, Miguel A" uniqKey="Fuentes M" first="Miguel A" last="Fuentes">Miguel A. Fuentes</name>
</noRegion>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Eau/explor/LotaV3/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000034 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000034 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Eau
   |area=    LotaV3
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     pubmed:26565183
   |texte=   First-passage times for pattern formation in nonlocal partial differential equations.
}}

Pour générer des pages wiki

HfdIndexSelect -h $EXPLOR_AREA/Data/Main/Exploration/RBID.i   -Sk "pubmed:26565183" \
       | HfdSelect -Kh $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd   \
       | NlmPubMed2Wicri -a LotaV3

This area was generated with Dilib version V0.6.39.
Data generation: Fri May 20 09:58:26 2022. Site generation: Fri May 20 10:24:07 2022

Serveur d'exploration Lota lota

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

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

Source :

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri

Pour générer des pages wiki

	Serveur d'exploration Lota lota
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.