Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/131167
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dc.contributor.authorBunder, J.E.en
dc.contributor.authorRoberts, A.J.en
dc.date.issued2021en
dc.identifier.citationSN Applied Sciences, 2021; 3(7):703-1-703-28en
dc.identifier.issn2523-3963en
dc.identifier.issn2523-3971en
dc.identifier.urihttp://hdl.handle.net/2440/131167-
dc.description.abstractMany multiscale physical scenarios have a spatial domain which is large in some dimensions but relatively thin in other dimensions. These scenarios includes homogenization problems where microscale heterogeneity is effectively a ‘thin dimension’. In such scenarios, slowly varying, pattern forming, emergent structures typically dominate the large dimensions. Common modelling approximations of the emergent dynamics usually rely on self-consistency arguments or on a nonphysical mathematical limit of an infinite aspect ratio of the large and thin dimensions. Instead, here we extend to nonlinear dynamics a new modelling approach which analyses the dynamics at each cross-section of the domain via a multivariate Taylor series (Roberts and Bunder in IMA J Appl Math 82(5):971–1012, 2017. https:// doi. org/ 10. 1093/ imamat/ hxx021). Centre manifold theory extends the analysis at individual cross-sections to a rigorous global model of the system’s emergent dynamics in the large but finite domain. A new remainder term quantifies the error of the nonlinear modelling and is expressed in terms of the interaction between cross-sections and the fast and slow dynamics. We illustrate the rigorous approach by deriving the large-scale nonlinear dynamics of a thin liquid film on a rotating substrate. The approach developed here empowers new mathematical and physical insight and new computational simulations of previously intractable nonlinear multiscale problems.en
dc.description.statementofresponsibilityJ. E. Bunder, A. J. Robertsen
dc.language.isoenen
dc.publisherSpringeren
dc.rights© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.en
dc.subjectNonlinear dynamics; Emergent dynamics; Centre manifold theory; Multiscale modelling; Computational fluid dynamicsen
dc.titleNonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systemsen
dc.typeJournal articleen
dc.identifier.doi10.1007/s42452-021-04229-9en
dc.relation.granthttp://purl.org/au-research/grants/arc/DP150102385en
dc.relation.granthttp://purl.org/au-research/grants/arc/DP180100050en
pubs.publication-statusPublisheden
dc.identifier.orcidBunder, J.E. [0000-0001-5355-2288]en
dc.identifier.orcidRoberts, A.J. [0000-0001-8930-1552]en
Appears in Collections:Mathematical Sciences publications

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