Optimal channel networks
Luca Giaccone
Optimal channel networks.
Rel. Luca Ridolfi, Amilcare Porporato. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2023
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Abstract
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
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