We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every d ≥ 2. Results extend our capabilities in environmental statistical mechanics.

River landscapes and optimal channel networks

Bollobas B.;Caldarelli G.;Mastrandrea R.;Morris R.;
2018

Abstract

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for every d ≥ 2. Results extend our capabilities in environmental statistical mechanics.
Graph theory
River networks
Spanning trees
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11771/16317
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