Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: nonstandard scaling

King, John R.; Köry, Jakub; Ptashnyk, Mariya

Abstract

In this paper we undertake a multiscale analysis of nutrient uptake by plant roots by considering different scale relations between the radius of root hairs and the distance between them. We combine the method of formal asymptotic expansions and rigorous derivation of macroscopic equations. The former prompt us to study a distinguished limit (which yields a distinct effective equation), allow us to determine higher-order correctors, and provide motivation for the construction of correctors essential for rigorous derivation of macroscopic equations. The results of our asymptotic analysis are validated by direct comparison with full-geometry numerical simulations.

Citation

King, J. R., Köry, J., & Ptashnyk, M. (2021). Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: nonstandard scaling. SIAM Journal on Applied Mathematics, 81(4), 1361-1388. https://doi.org/10.1137/19M1309626

• Journal Article Type: Article
• Acceptance Date: Mar 30, 2021
• Online Publication Date: Jul 12, 2021
• Publication Date: 2021
• Deposit Date: Apr 25, 2021
• Publicly Available Date: Jul 12, 2021
• Journal: SIAM Journal on Applied Mathematics
• Print ISSN: 0036-1399
• Electronic ISSN: 1095-712X
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 81
• Issue: 4
• Pages: 1361-1388
• DOI: https://doi.org/10.1137/19M1309626
• Keywords: Homogenization; parabolic equations; nutrient uptake by plants; sparse root hairs; nonstandard scaling; domains perforated by very thin tubes
• Public URL: https://nottingham-repository.worktribe.com/output/5495882
• Publisher URL: https://epubs.siam.org/doi/10.1137/19M1309626