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Generalization of the Fractal Einstein Law Relating Conduction and Diffusion on Networks
Physical Review Letters
We settle a long-standing controversy about the exactness of the fractal Einstein and Alexander-Orbach laws by showing that the properties of a class of fractal trees violate both laws. A new formula is derived which unifies the two classical results by showing that if one holds, then so must the other, and resolves a puzzling discrepancy in the properties of Eden trees and diffusion-limited aggregates. We also conjecture that the result holds for networks which have no fractal dimension. Thedoi:10.1103/physrevlett.103.020601 pmid:19659194 fatcat:hetfgr47b5g5ho5xsy3t3p4vbi