Abstract
Simple conditions are presented under which the fractal dimension of a random walk on an aggregate, dw, is given by dw=D+1, where D is the aggregate's fractal dimension. These conditions are argued (with one simple speculative assumption) to apply for D<2, implying a breakdown of the Alexander-Orbach rule dw=3D2. Existing results for percolation clusters, lattice animals, and diffusion-limited aggregates seem to favor our new rule.
Original language | English |
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Pages (from-to) | 2368-2370 |
Number of pages | 3 |
Journal | Physical Review Letters |
Volume | 52 |
Issue number | 26 |
DOIs | |
State | Published - 1 Jan 1984 |
Externally published | Yes |
ASJC Scopus subject areas
- General Physics and Astronomy