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

  1. homogenization
  2. parabolic equations
  3. nutrient uptake by plants
  4. sparse root hairs
  5. nonstandard scaling
  6. domains perforated by very thin tubes

MSC codes

  1. 35Bxx
  2. 35K20
  3. 35Q92
  4. 35K60
  5. 92C80

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Supplementary Material


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Title of paper: Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: Nonstandard scaling

Authors: John King, Jakub Kory, and Mariya Ptashnyk

File: KKPsupplement.pdf

Type: PDF

Contents: We provide the non-dimensionalisation of the model equations considered in the manuscript, some additional details on the derivation of the macroscopic equations in the case of non-linear boundary conditions, by using formal asymptotic expansion, and a figure depicting isosurfaces of nutrient concentration around root hairs.

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Information & Authors

Information

Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 1361 - 1388
ISSN (online): 1095-712X

History

Submitted: 30 December 2019
Accepted: 30 March 2021
Published online: 12 July 2021

Keywords

  1. homogenization
  2. parabolic equations
  3. nutrient uptake by plants
  4. sparse root hairs
  5. nonstandard scaling
  6. domains perforated by very thin tubes

MSC codes

  1. 35Bxx
  2. 35K20
  3. 35Q92
  4. 35K60
  5. 92C80

Authors

Affiliations

Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : 294729

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