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Generalization of the Fractal Einstein Law Relating Conduction and Diffusion on Networks

Christophe P. Haynes, Anthony P. Roberts
2009 Physical Review Letters  

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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. The
more » ... ilure of the classical laws is attributed to anisotropic exploration of the network by a random walker. The occurrence of this newly revealed behavior means that the conventional laws must be checked if they, or numerous results which depend on them, are to be applied accurately.
doi:10.1103/physrevlett.103.020601 pmid:19659194 fatcat:hetfgr47b5g5ho5xsy3t3p4vbi
Citation

Christophe P. Haynes, Anthony P. Roberts. "Generalization of the Fractal Einstein Law Relating Conduction and Diffusion on Networks." Physical Review Letters 103.2 (2009)