On a Shape Optimization Problem for Tree Branches

TL;DR

This paper investigates a shape optimization problem for tree branches, aiming to maximize sunlight collection while minimizing water and nutrient transport costs, with a complete solution in two dimensions.

Contribution

The paper provides a unique and explicit solution to a shape optimization problem modeling tree branch structures in 2D.

Findings

Solution is unique in 2D

Explicitly determined optimal shape

Balances sunlight collection and transport costs

Abstract

This paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of the trunk to all the leaves. In the case of 2 space dimensions, the solution is proved to be unique, and explicitly determined.