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A minimalist model for coevolving supply and drainage networks

Authors :
Shashank Kumar Anand
Milad Hooshyar
Jan Martin Nordbotten
Amilcare Porporato
Source :
Royal Society Open Science, Vol 8, Iss 2 (2021)
Publication Year :
2021
Publisher :
The Royal Society, 2021.

Abstract

Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here, we present a minimalist model of such coevolving networks in a spatially continuous domain, where the obtained networks can be interpreted as a part of either the counter-flowing drainage or co-flowing supply and drainage mechanisms. The model consists of three coupled, nonlinear partial differential equations that describe spatial density patterns of input and output materials by modifying a mediating scalar field, on which supply and drainage networks are carved. In the two-dimensional case, the scalar field can be viewed as the elevation of a hypothetical landscape, of which supply and drainage networks are ridges and valleys, respectively. In the three-dimensional case, the scalar field serves the role of a chemical signal, according to which vascularization of the supply and drainage networks occurs above a critical ‘erosion’ strength. The steady-state solutions are presented as a function of non-dimensional channelization indices for both materials. The spatial patterns of the emerging networks are classified within the branched and congested extreme regimes, within which the resulting networks are characterized based on the absolute as well as the relative values of two non-dimensional indices.

Details

Language :
English
ISSN :
20545703
Volume :
8
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Royal Society Open Science
Publication Type :
Academic Journal
Accession number :
edsdoj.9ebb60f9bdc44e60bb9bddff86ec8e9d
Document Type :
article
Full Text :
https://doi.org/10.1098/rsos.201407