@article{308dc3915a1a4512a6617acec2bbb6da,
title = "Multiscale Analysis of Nutrient Uptake by Plant Roots with Sparse Distribution of Root Hairs: Nonstandard Scaling",
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.",
keywords = "Domains perforated by very thin tubes, Homogenization, Nonstandard scaling, Nutrient uptake by plants, Parabolic equations, Sparse root hairs",
author = "King, {John R.} and Jakub K{\"o}ry and Mariya Ptashnyk",
note = "Funding Information: \ast Received by the editors December 30, 2019; accepted for publication (in revised form) March 30, 2021; published electronically July 12, 2021. https://doi.org/10.1137/19M1309626 Funding: JRK and JK were supported by FUTUREROOTS Project (project ID 294729) between the European Research Council and the University of Nottingham. \dagger School of Mathematical Sciences and Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Nottingham NG7 2RD, UK (john.king@nottingham.ac.uk). \ddagger School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK (Jakub.Koery@glasgow.ac.uk). \S School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AL, UK (m.ptashnyk@hw.ac.uk). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2021",
month = jul,
day = "12",
doi = "10.1137/19M1309626",
language = "English",
volume = "81",
pages = "1361–1388",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}