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 journalArticlepeer-review

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 languageEnglish
Pages (from-to)1361–1388
Number of pages28
JournalSIAM Journal on Applied Mathematics
Volume81
Issue number4
DOIs
Publication statusPublished - 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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