A surface model of nonlinear, non-steady-state phloem transport

Youcef Mammeri; Damien Sellier; Youcef Mammeri; Damien Sellier

doi:10.3934/mbe.2017055

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 4: 1055-1069. doi: 10.3934/mbe.2017055

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A surface model of nonlinear, non-steady-state phloem transport

Youcef Mammeri ^{1
,
,},
Damien Sellier ²

1.
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80069 Amiens, France
2.
SCION, New Zealand Forest Research Institute, Private bag 3020, Rotorua 3046, New Zealand

Received: 01 April 2016 Accepted: 01 February 2017 Published: 01 August 2017
MSC : Primary: 35K61, 92C80; Secondary: 65M60

Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties. Those features represent an significant advance in modelling the pathway for carbohydrate transport in trees.
- Phloem transport,
- diffusion-convection equation,
- well-posedness,
- finite elements
Citation: Youcef Mammeri, Damien Sellier. A surface model of nonlinear, non-steady-state phloem transport[J]. Mathematical Biosciences and Engineering, 2017, 14(4): 1055-1069. doi: 10.3934/mbe.2017055

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Abstract

Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties. Those features represent an significant advance in modelling the pathway for carbohydrate transport in trees.

References

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