<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "River Networks and Optimal Channel Networks"^^ . "River networks represent a perfect example of a physical\r\nphenomenon that can be described by means of graph theory.\r\nWater collected by rainfall flows from one point to another\r\none (downstream) in the river basin creates a spanning (water\r\nflows uniformly on the terrain and therefore from every point\r\nof the basin we have water flow) tree (water cannot flow uphill).\r\nRivers on Earth and even those that might have been\r\npresent on Mars all display similar statistical properties\r\nthereby calling for a model based on basic properties. \r\nA class of models named Optimal Channel Networks (OCN) derive \r\nthe final configuration by minimising a given cost function.\r\nThe physical inspiration for the minimization problem traces\r\nback to the ideas of Nobel laureate Prigogine on a general\r\ntheory of irreversible processes in open dissipative systems.\r\nActually, theoretical results from OCN allowed to provide an\r\nexplanation to universal allometric behaviour in a variety\r\nof different physical situations from species distribution to food webs optimisation alternative to the traditional\r\napproach. In the specific case of river networks, the OCN\r\nmodel postulates that the total gravitational energy loss in the\r\nsystem is minimised. Empirical and theoretical works focus\r\ngenerally on two dimensional case, while recently (inspired by\r\nvascular systems) also the three dimensional case has been\r\nanalysed.\r\nHere we devise some new analytical results that illustrate\r\nthe role and the properties of the structure that minimises\r\nthe cost function proposed in the ABM and we also provide\r\nsome insight about the structure of the absolute minimum by varying some of the parameters of the model. In what follows we will give a theoretical characterization of river networks and provide a simple rule to distinguish spanning trees from natural river trees. Furthermore, we extend the study of OCNs embedded on a lattice finding a lower and upper bound for the energy of an OCN in any dimension D."^^ . . . . . . . . . . . . . . . . . . . . . . "Rossana"^^ . "Mastrandrea"^^ . "Rossana Mastrandrea"^^ . . "Rob"^^ . "Morris"^^ . "Rob Morris"^^ . . "Guido"^^ . "Caldarelli"^^ . "Guido Caldarelli"^^ . . "Paul"^^ . "Balister"^^ . "Paul Balister"^^ . . "Jószef"^^ . "Balogh"^^ . "Jószef Balogh"^^ . . "Béla"^^ . "Bollobás"^^ . "Béla Bollobás"^^ . . . . . "HTML Summary of #3738 \n\nRiver Networks and Optimal Channel Networks\n\n" . "text/html" . . . "QA Mathematics"@en . . . "QC Physics"@en . .