Diffusion on asymmetric fractal networks
Statistical Mechanics
2015-05-13 v1
Abstract
We derive a renormalization method to calculate the spectral dimension of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of microstructural details to be quantitatively investigated. In addition to providing new models for physical networks, the results allow precise tests of theories of diffusive transport. For example, the properties of a class of non-recurrent trees () with asymmetric elements and branching violate the Alexander Orbach scaling law.
Cite
@article{arxiv.0904.3791,
title = {Diffusion on asymmetric fractal networks},
author = {Christophe P. Haynes and Anthony P. Roberts},
journal= {arXiv preprint arXiv:0904.3791},
year = {2015}
}