Glass transition seen through asymptotic expansions

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dc.contributorVirginia Techen
dc.contributor.authorOlivier, J.en
dc.contributor.authorRenardy, Michael J.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:00Zen
dc.date.available2014-05-28T18:35:00Zen
dc.date.issued2011en
dc.description.abstractSoft glassy materials exhibit the so-called glassy transition, which means that the behavior of the model at a low shear rate changes when a certain parameter (which we call the glass parameter) crosses a critical value. This behavior goes from a Newtonian behavior to a Herschel-Bulkley behavior through a power-law-type behavior at the transition point. In a previous paper we rigorously proved that the Hebraud-Lequeux model, a Fokker-Planck-like description of soft glassy material, exhibits such a glass transition. But the method we used was very specific to the one-dimensional setting of the model, and as a preparation for generalizing this model to take into account multidimensional situations, we look for another technique to study the glass transition of this type of model. In this paper we shall use matched asymptotic expansions for such a study. The difficulties encountered when using asymptotic expansions for the Hebraud-Lequeux model are that multiple ansaetze have to be used, even though the initial model is unique, due to the glass transition. We shall delineate the various regimes and give a rigorous justification of the expansion by means of an implicit function argument. The use of a two parameter expansion plays a crucial role in elucidating the reasons for the scalings which occur.en
dc.description.sponsorshipANR ANR-08-SYSC-010en
dc.description.sponsorshipNational Science Foundation DMS-1008426en
dc.identifier.citationOlivier, J.; Renardy, M., "Glass transition seen through asymptotic expansions," SIAM J. Appl. Math., 71(4), 1144-1167, (2011). DOI: 10.1137/100800725en
dc.identifier.doihttps://doi.org/10.1137/100800725en
dc.identifier.issn0036-1399en
dc.identifier.urihttp://hdl.handle.net/10919/48131en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/100800725en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectglass transitionen
dc.subjectboundary layersen
dc.subjectimplicit functionsen
dc.subjectlinearen
dc.subjectperturbationen
dc.subjectpenalization methoden
dc.subjectrheologyen
dc.subjectequationen
dc.subjectflowsen
dc.subjectmathematics, applieden
dc.titleGlass transition seen through asymptotic expansionsen
dc.title.serialSiam Journal on Applied Mathematicsen
dc.typeArticle - Refereeden

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