Please use this identifier to cite or link to this item:
Scopus Web of Science® Altmetric
Type: Journal article
Title: Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains
Author: Roberts, A.
Bunder, J.
Citation: IMA Journal of Applied Mathematics, 2017; 82(5):971-1012
Publisher: Oxford University Press
Issue Date: 2017
ISSN: 0272-4960
Statement of
A. J. Roberts and J. E. Bunder
Abstract: Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario, we typically expect the system to have emergent structures that vary slowly over the large dimensions. For practical mathematical modelling of such systems we require efficient and accurate methodologies for reducing the dimension of the original system and extracting the emergent dynamics. Common mathematical approximations for determining the emergent dynamics often rely on self-consistency arguments or limits as the aspect ratio of the ‘large’ and ‘thin’ dimensions becomes unphysically infinite. Here we build on a new approach, previously establish for systems which are large in only one dimension, which analyses the dynamics at each cross-section of the domain with a rigorous multivariate Taylor series. Then centre manifold theory supports the local modelling of the system’s emergent dynamics with coupling to neighbouring cross-sections treated as a non-autonomous forcing. The union over all cross-sections then provides powerful support for the existence and emergence of a centre manifold model global in the large finite domain. Quantitative error estimates are determined from the interactions between the cross-section coupling and both fast and slow dynamics. Two examples provide practical details of our methodology. The approach developed here may be used to quantify the accuracy of known approximations, to extend such approximations to mixed order modelling, and to open previously intractable modelling issues to new tools and insights.
Keywords: Multiple scales; thin domain; slowly varying; centre manifold theory
Description: Advance Access Publication on 5 July 2017
Rights: © The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
DOI: 10.1093/imamat/hxx021
Grant ID:
Published version:
Appears in Collections:Aurora harvest 3
Mathematical Sciences publications

Files in This Item:
There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.