title: Continuum diffusion on networks: trees with hyperbranched trunks and fractal branches.
abstract: The probability that a random walker returns to its origin for large times scales as t;{-d[over ]2} , where d[over ] is the spectral dimension. We calculate d[over ] for a class of tree structures using a renormalization technique on an infinite continued fraction. We consider a wide range of homogeneous networks based on replacing the branches of a self-similar tree with arbitrary fractals and composite fractals. We also consider a new class of inhomogeneous hyperbranched trees.
authors.affiliation: School of Mathematics and Physics, University of Queensland, Queensland 4072, Australia.
authors.forename: C P
authors.initials: CP
authors.lastname: Haynes
authors.forename: A P
authors.initials: AP
authors.lastname: Roberts