期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2018
卷号：115
期号：26
页码：6548-6553
DOI：10.1073/pnas.1804484115
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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
关键词：spanning trees ; graph theory ; slope-area law ; landscape evolution
