Generalisation of the fractal Einstein law relating conduction and diffusion on networks
| dc.creator | Roberts, Anthony P. | |
| dc.creator | Haynes, Christophe P. | |
| dc.date | 2009-03-19 | |
| dc.date.accessioned | 2026-07-07T12:54:13Z | |
| dc.date.available | 2026-07-07T12:54:13Z | |
| dc.description | In the 1980s an important goal of the emergent field of fractals was to determine the relationships between their physical and geometrical properties. The fractal-Einstein and Alexander-Orbach laws, which interrelate electrical, diffusive and fractal properties, are two key theories of this type. Here we settle a long standing controversy about their exactness 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 proving that if one holds, then so must the other, and resolves a puzzling discrepancy in the properties of Eden trees and diffusion limited aggregates. The failure of the classical laws is attributed to anisotropic exploration of the network by a random walker. The occurrence of this newly revealed behaviour means that numerous theories, such as recent first passage time results, are restricted to a narrower range of networks than previously thought. | |
| dc.identifier | https://arxiv.org/abs/0903.3279 | |
| dc.identifier | http://arxiv.org/abs/0903.3279 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223855 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Generalisation of the fractal Einstein law relating conduction and diffusion on networks | |
| dc.type | text |