Optimal transport from a point-like source

Cardin, Franco; Banavar, Jayanth R.; Maritan, Amos

doi:10.1007/s00161-019-00844-5

Continuum Mech. Thermodyn.

2019

DOI: 10.1007/s00161-019-00844-5

|View full text |Cite

Optimal transport from a point-like source

Franco Cardin

Jayanth R. Banavar

Amos Maritan

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[21][22][23][24]. Recently, there have been efforts to interpret this static principle as the result of a dynamic evolution based on partial differential equation (PDE) [25][26][27][28].…”

mentioning

confidence: 99%

A minimalist model for coevolving supply and drainage networks

et al. 2021

View full text Add to dashboard Cite

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.

show abstract

“…[21][22][23][24]. Recently, there have been efforts to interpret this static principle as the result of a dynamic evolution based on partial differential equation (PDE) [25][26][27][28].…”

mentioning

confidence: 99%

A minimalist model for coevolving supply and drainage networks

et al. 2021

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Optimal transport from a point-like source

Cited by 1 publication

References 18 publications

A minimalist model for coevolving supply and drainage networks

A minimalist model for coevolving supply and drainage networks

Contact Info

Product

Resources

About