title: Universal scaling of optimal current distribution in transportation networks.
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.
authors.affiliation: Dipartimento di Fisica Galileo Galilei, CNISM and INFN, Università di Padova, 35131 Padova, Italy. simini@pd.infn.it
authors.forename: Filippo
authors.initials: F
authors.lastname: Simini
authors.forename: Andrea
authors.initials: A
authors.lastname: Rinaldo
authors.forename: Amos
authors.initials: A
authors.lastname: Maritan