Generalization of the fractal Einstein law relating conduction and diffusion on networks

Haynes, Christophe P. and Roberts, Anthony P. (2009) Generalization of the fractal Einstein law relating conduction and diffusion on networks. Physical Review Letters, 103 2: 020601-1-020601-4. doi:10.1103/PhysRevLett.103.020601

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Author Haynes, Christophe P.
Roberts, Anthony P.
Title Generalization of the fractal Einstein law relating conduction and diffusion on networks
Journal name Physical Review Letters   Check publisher's open access policy
ISSN 0031-9007
Publication date 2009-07
Sub-type Article (original research)
DOI 10.1103/PhysRevLett.103.020601
Open Access Status File (Publisher version)
Volume 103
Issue 2
Start page 020601-1
End page 020601-4
Total pages 4
Editor George Basbas
Jack Sandweiss
Reinhardt B. Schuhmann
Stanley G. Brown
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2010
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010404 Probability Theory
020304 Thermodynamics and Statistical Physics
Abstract 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 failure 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
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
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Citation counts: TR Web of Science Citation Count  Cited 12 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 10 times in Scopus Article | Citations
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Created: Tue, 30 Mar 2010, 11:53:54 EST by Kay Mackie on behalf of School of Mathematics & Physics