Optimal channel networks

Channel networks are ubiquitous in our world. They are found in biological systems as intricate blood capillary structures, in natural landscapes as river drainage patterns, and even in various human transport designs such as urban water supply networks. This thesis embarks on a comprehensive exploration of over a century of Optimal Channel Networks (OCNs) literature. Our aim is to formulate a unified model that encapsulates and generalizes the cumulative efforts in this domain. In our pursuit of this ambitious endeavor, we have provided a more robust mathematical description of the optimization process, revealing that the commonly assumed 'principle of local optimality' is, in fact, dispensable. Our generalization not only synthesizes the existing knowledge about optimal networks but also introduces fresh perspectives, including a modern picture of the optimal network landscape and the revelation of a phase transition within the ground state topology of these networks. This breakthrough enhances our understanding of the intricate interplay between channel networks structure and optimization, shedding light on previously unexplored facets of this fascinating field.