Multiscale Analysis of Nutrient Uptake by Plant Roots with Sparse Distribution of Root Hairs: Nonstandard Scaling

John R. King; Jakub Köry; Mariya Ptashnyk

doi:10.1137/19M1309626

Multiscale Analysis of Nutrient Uptake by Plant Roots with Sparse Distribution of Root Hairs: Nonstandard Scaling

John R. King
, Jakub Köry
, Mariya Ptashnyk

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

126 Downloads (Pure)

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.

Original language	English
Pages (from-to)	1361–1388
Number of pages	28
Journal	SIAM Journal on Applied Mathematics
Volume	81
Issue number	4
DOIs	https://doi.org/10.1137/19M1309626
Publication status	Published - 12 Jul 2021

Keywords

Domains perforated by very thin tubes
Homogenization
Nonstandard scaling
Nutrient uptake by plants
Parabolic equations
Sparse root hairs

ASJC Scopus subject areas

Applied Mathematics

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10.1137/19M1309626

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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",

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note = "Funding Information: \textbackslash{}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. \textbackslash{}dagger School of Mathematical Sciences and Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Nottingham NG7 2RD, UK ([email protected]). \textbackslash{}ddagger School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK ([email protected]). \textbackslash{}S School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AL, UK ([email protected]). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.",

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T2 - Nonstandard Scaling

AU - King, John R.

AU - Köry, Jakub

AU - Ptashnyk, Mariya

N1 - 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 ([email protected]). \ddagger School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK ([email protected]). \S School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AL, UK ([email protected]). Publisher Copyright: © 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.

PY - 2021/7/12

Y1 - 2021/7/12

N2 - 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.

AB - 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.

KW - Domains perforated by very thin tubes

KW - Homogenization

KW - Nonstandard scaling

KW - Nutrient uptake by plants

KW - Parabolic equations

KW - Sparse root hairs

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DO - 10.1137/19M1309626

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EP - 1388

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

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ER -

Multiscale Analysis of Nutrient Uptake by Plant Roots with Sparse Distribution of Root Hairs: Nonstandard Scaling

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