Geometry And Topology Of Optimal Flow Networks

Hidden inside the design of a living network is the key to its function: above all else, nature searches for a pathway to survival. Every naturally evolved network is a step in the path to reach an optimized state, even if it has not yet been achieved, and in the physicist's view, some energy function that is in the process of becoming minimized. The problem is figuring what exactly is being minimized, weighing the contributions from operational costs, performance, and robustness to disturbances. Understanding the structural rules for these networks has profound implications for artificial network design in fields ranging from transportation to medicine. The focus of this work is transport networks in biological systems, specifically plant and animal vasculature. The overarching themes are adaptation, optimality, and the link between structure and function in complex networks. We first examine hierarchy in networks, showing that such organization may allow networks to maintain functionality in unstable conditions such as perturbative damage or fluctuating loads. We then turn our attention to principles of optimization in perfusive flow networks. We show that including perfusion dynamics on top of the simple flow equations allows us to identify the geometric rules controlling the structure of uniformly perfusing networks.