@article{d710fea410d6402c8660a0f36acc36e2,
title = "River landscapes and optimal channel networks",
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.",
keywords = "Graph theory, Landscape evolution, Slope-area law, Spanning trees",
author = "Paul Balister and J{\'o}zsef Balogh and Enrico Bertuzzo and B{\'e}la Bollob{\'a}s and Guido Caldarelli and Amos Maritan and Rossana Mastrandrea and Robert Morris and Andrea Rinaldo",
note = "Funding Information: R : i∈R R : i−1∈R sinceci(1)∈V{i},soV{i}∕ ∅.Settingαi:=R:i∈R∑αR,itfollowsthatα1> α2 > · · · > αk > α1, which is the desired contradiction. □ ACKNOWLEDGMENTS. P.B. and B.B. are partly supported by NSF Grant DMS 1600742. J.B. is partly supported by NSF Grant DMS-1500121 and an Arnold O. Beckman Research Award (University of Illinois Urbana– Champaign Campus Research Board 15006). B.B. and G.C. are partially supported by MULTIPLEX Grant 317532. R. Morris is partially supported by Brazilian National Council for Scientific and Technological Development Grant 303275/2013-8, Fundac¸{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa do Estado do Rio de Janeiro Grant 201.598/2014, and European Research Council (ERC) Starting Grant 680275 MALIG. A.R. and E.B. have been supported by ERC Advanced Grant RINEC 22761. Part of the research in this paper was carried out while J.B. was a Visiting Fellow Commoner at Trinity College, Cambridge. Funding Information: P.B. and B.B. are partly supported by NSF Grant DMS 1600742. J.B. is partly supported by NSF Grant DMS-1500121 and an Arnold O. Beckman Research Award (University of Illinois Urbana–Champaign Campus Research Board 15006). B.B. and G.C. are partially supported by MULTIPLEX Grant 317532. R. Morris is partially supported by Brazilian National Council for Scientific and Technological Development Grant 303275/2013-8, Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa do Estado do Rio de Janeiro Grant 201.598/2014, and European Research Council (ERC) Starting Grant 680275 MALIG. A.R. and E.B. have been supported by ERC Advanced Grant RINEC 22761. Part of the research in this paper was carried out while J.B. was a Visiting Fellow Commoner at Trinity College, Cambridge. Publisher Copyright: {\textcopyright} 2018 National Academy of Sciences. All Rights Reserved.",
year = "2018",
month = jun,
day = "26",
doi = "10.1073/pnas.1804484115",
language = "English (US)",
volume = "115",
pages = "6548--6553",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
publisher = "National Academy of Sciences",
number = "26",
}