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

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

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.

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Keywords Phloem transport; diffusion-convection equation; well-posedness; finite elements

Citation: Youcef Mammeri, Damien Sellier. A surface model of nonlinear, non-steady-state phloem transport. Mathematical Biosciences and Engineering, 2017, 14(4): 1055-1069. doi: 10.3934/mbe.2017055


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