Phase transitions in transportation networks with nonlinearities.
We investigate a model of transportation networks with nonlinear elements which may represent local shortage of resources. Frustrations arise from competition for resources. When the initial resources are uniform, different regimes with discrete fractions of satisfied nodes are observed, resembling the Devil's staircase. We demonstrate how functional recursions are converted to simple recursions of probabilities. Behaviors similar to those in the vertex cover or close packing problems are found. When the initial resources are bimodally distributed, increases in the fraction of rich nodes induce a glassy transition, entering an algorithmically hard regime.
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China.
C H
CH
Yeung
K Y Michael
KY
Wong