Bhattacharya, P. orcid.org/0000-0003-1109-1174, Li, Q., Lacroix, D. et al. (2 more authors) (2021) A systematic approach to the scale separation problem in the development of multiscale models. PLoS ONE, 16 (5). e0251297. ISSN 1932-6203
Abstract
Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such ‘multiscale’ problems, that of defining a ‘scale’ remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2021 Bhattacharya et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Mechanical Engineering (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - HORIZON 2020 675451 CompBioMed ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/S032940/1 EUROPEAN COMMISSION - HORIZON 2020 823712 Engineering and Physical Sciences Research Council EP/K03877X/1 National Institute for Health Research NIHRDH-IS-BRC-1215-20017 EUROPEAN COMMISSION - HORIZON 2020 857533 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Jun 2021 16:26 |
Last Modified: | 07 Jun 2021 16:26 |
Status: | Published |
Publisher: | Public Library of Science (PLoS) |
Refereed: | Yes |
Identification Number: | 10.1371/journal.pone.0251297 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:174696 |