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 sub-structures.
The talk is based on: P. Balister, J. Balogh, E. Bertuzzo, B. Bollobas, G. Caldarelli, A. Maritan, R. Mastrandrea, R. Morris, A Rinaldo: River landscapes and Optimal Channel Networks, Proceeding of the National Academy of Sciences U.S.A., 115, 6548--6553 (2018).
This paper is based on a true collaboration among mathematicians, theoretical computer scientists and physicists.