A diagram of the optimal branching structures for systems with fixed "sinks" — nodes where the flow branches further down the path.
Image Credit: Dan Hu/David Cai/PRL
Branching structures crop up in a number of biological applications, such as the veins in leaves that transport water or the veins in our bodies that transport blood.
Past research has suggested that the structure of these networks tends to minimize energy consumption, leading to the most efficient transport systems. With this in mind, a physicist and mathematician — Dan Hu (Shanghaio Jiao Tong University) and David Cai (Courant Institute) — teamed up to model what these optimal structures would look like.
The image above shows part of the team's work. In the image, fluid flows from the bottommost central node and flows outward just like in a leaf. In this case, the nodes (branching points) were fixed so that the amount of fluid that could flow through them remained constant.