Root growth: homogenization in domains with time dependent partial perforations

Yves Capdeboscq; Mariya Ptashnyk

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 3, page 856-876
  • ISSN: 1292-8119

Abstract

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In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for the nutrient density.

How to cite

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Capdeboscq, Yves, and Ptashnyk, Mariya. "Root growth: homogenization in domains with time dependent partial perforations." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 856-876. <http://eudml.org/doc/277819>.

@article{Capdeboscq2012,
abstract = {In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for the nutrient density. },
author = {Capdeboscq, Yves, Ptashnyk, Mariya},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; root growth; time dependent domains; time-dependent boundaries; PDE-ODE system},
language = {eng},
month = {11},
number = {3},
pages = {856-876},
publisher = {EDP Sciences},
title = {Root growth: homogenization in domains with time dependent partial perforations},
url = {http://eudml.org/doc/277819},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Capdeboscq, Yves
AU - Ptashnyk, Mariya
TI - Root growth: homogenization in domains with time dependent partial perforations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
PB - EDP Sciences
VL - 18
IS - 3
SP - 856
EP - 876
AB - In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for the nutrient density.
LA - eng
KW - Homogenization; root growth; time dependent domains; time-dependent boundaries; PDE-ODE system
UR - http://eudml.org/doc/277819
ER -

References

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