Mathematics of Living Matter – Abstracts

9:15 AM – 10:00 AM, Thursday, October 18, 2018; Room: 114 McAllister bldg.

On the optimal shape of tree roots and branches

Alberto Bressan, The Pennsylvania State University, USA

Living organisms come in an immense variety of shapes. In many cases one may expect that, through natural selection, a “best possible” shape will have evolved. From a mathematical perspective, it is thus of interest to study functionals whose minimizers correspond to some of the many shapes found in the biological world.

As a step in this direction, we consider two functionals measuring the efficiency of roots and branches in a tree.

The first one, which we call the “sunlight functional”, models the total amount of sunlight captured by the leaves. The second one, which we call the “harvest functional”, models the amount of nutrients collected by the roots. The above functionals can be combined with a “ramified transportation cost”, for transporting nutrients from the roots to the base of the trunk, or from the base of the trunk to the leaves.

The talk will address the semicontinuity of these functionals, and the existence and properties of optimal solutions, in a space of measures.

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