## Abstract

We discuss topologically biased diffusion on random structures (e.g. a random comb, a percolation cluster) that are characterized by effective dangling ends. The distribution of lengths L of dangling ends determines the transport behaviour. For a power-law distribution (percolation cluster at p_{c}) diffusion is ultra-anomalously slow, the mean square displacement of a random walker varies with a power law of logr, while for exponential distributions (p>p_{c}) a dynamical phase transition occurs: above a critical bias field £c diffusion is anomalous and non-universal. We also consider diffusion in d= 2 percolation clusters at criticality under the influence of a n'we-dependent bias field E(t) = E_{0} sin ωt. We discuss the mean displacement <x(t)> of a random walker and investigate strong nonlinear effects in the amplitude A(E_{0},ω) of <.x(t)> by computer simulation.

Original language | English |
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Pages (from-to) | 821-831 |

Number of pages | 11 |

Journal | Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties |

Volume | 56 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1987 |

### Bibliographical note

Funding Information:A.B. gratefully acknowledges financial support from Deutsche Forschungs-gemeinschaft, and S.H. support from the U.S.-Israel Bi-national Science Foundation and from a Minerva Fellowship.

### Funding

A.B. gratefully acknowledges financial support from Deutsche Forschungs-gemeinschaft, and S.H. support from the U.S.-Israel Bi-national Science Foundation and from a Minerva Fellowship.

Funders | Funder number |
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U.S.–Israel Bi-National Science Foundation | |

Deutsche Forschungsgemeinschaft |