English

Diffusion on asymmetric fractal networks

Statistical Mechanics 2015-05-13 v1

Abstract

We derive a renormalization method to calculate the spectral dimension dˉ\bar{d} 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 (dˉ>2\bar{d}>2) with asymmetric elements and branching violate the Alexander Orbach scaling law.

Keywords

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}
}
R2 v1 2026-06-21T12:54:40.481Z