Understanding Water Flow in Plants: Modeling and Analysis
Explore the intricate world of plant hydraulics and water balance through mathematical modeling, analogies to electric circuits, vulnerability curves, and the Richards equation. Unravel the complex dynamics of water flow in plants and the non-linear equations that govern them.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Modeling Water Flow in Plants Sergiy Koshkin UHD Mathematics and Statistics NSF REU grant #1560401
Plant Hydraulics Water balance ? = ?2 ?1= ?? Darcy s Law ?(?) ? = ?(?)(?2 ?1)=? F flow of water E evaporationrate L leaf area ? water potential (pressure) ?(?) conductance ?? ?2 ?2 ? ?1 ?1
Electric Circuit Analogy Kirchhoff s current law Ohm s law Computing flows and potentials is almost like solving electric circuits. But ? ? =1/R ?ishighly nonlinear in ?.
Vulnerability Curves ?(?) = ????? ? Weibull function fit: ? Stationary flow in segments is given by ? ??= ? ? ??, ? 1 and the integral can be expressed via the incomplete gamma function, incomplete gamma function, implemented in MATLAB and Maple. ?
Richards equation The truth holds partial derivatives and time. Water balance? = ?(?)?? ?? and Darcy s law?? ??= ?? ? ? + ??? ?? combine into the Richards equation: ??? ??= ? ???(?)?? ??+ ?? ?(?) This is a diffusion equation, but non-linear, unlike classical ones It is set on a graph (of a plant), not a classical domain
