Structure, Scaling, and Phase Transition in the Optimal Transport Network

Publisher Website
Google Scholar
Abstract
The structure and properties of optimal networks depend on the cost functional being minimized and on constraints to which the minimization is subject. We show here two different formulations that lead to identical results: minimizing the dissipation rate of an electrical network under a global constraint is equivalent to the minimization of a power-law cost function introduced by Banavar et al. [ Phys. Rev. Lett. 84, 4745 (2000)]. An explicit scaling relation between the currents and the corresponding conductances is derived, proving the potential flow nature of the latter. Varying a unique parameter, the topology of the optimized networks shows a transition from a tree topology to a very redundant structure with loops; the transition corresponds to a discontinuity in the slope of the power dissipation.
All Related Versions

This publication has 13 references indexed in Scilit: