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Updated: Aug 13, 2026

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
Universality of the optimal path in the strong disorder limit
Sergey V Buldyrev1, Shlomo Havlin, Eduardo López
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Abstract:
We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length l of the optimal path scales with geometric distance r , as l approximately r (d(opt) ) with d(opt) =1.22+/-0.01 for d=2 and 1.44+/-0.02 for d=3 , independent of whether the optimization is on a path of weighted bonds or sites, and independent of the lattice or its coordination number. Our finding suggests that the exponent d(opt) is universal, depending only on the dimension of the system.
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