## Abstract

We consider a fractal network of nonlinear resistors, with the voltage V behaving as a power of;he current I, V= RI^{α}. The resistance between two points at a distance L is R(L)δ L^{ξ(α)}. We prove that ξ(δ) describes the scaling of the topological-chemical distance, while i(m) describes that of the number of singly connected ‘red’ bonds. -For random resistors, y e also consider the width of the resistance distribution, ΔRδ L^{ξ}_{2}^{(α)}. Values for ξ and ξ_{2} are explicitly derived for two model fractals, and ΔR/R is found to grow with L for the Sierpinski gasket and a > 1.612. The relevance of the results to percolation clusters is discussed.

Original language | English |
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Pages (from-to) | L443-L448 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 18 |

Issue number | 8 |

DOIs | |

State | Published - 1 Jun 1985 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy