Universal scaling of optimal current distribution in transportation networks

Filippo Simini*, Andrea Rinaldo, Amos Maritan

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected d-dimensional network exhibit robust scale-invariance properties, independently of the particular cost function considered, as long as it is convex. We find that, in the limit of large currents, the distribution decays as a power law with an exponent equal to (2d-1)/(d-1). The current distribution can be exactly calculated in d=2 for all values of the current. Numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions.

Original languageEnglish
Article number046110
Number of pages5
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number4
DOIs
Publication statusPublished - Apr 2009

Keywords

  • RIVER NETWORKS
  • ENERGY
  • AGGREGATION
  • transport processes
  • OPTIMAL CHANNEL NETWORKS
  • complex networks
  • FRACTAL STRUCTURES
  • OPTIMIZATION

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