Many geophysical and atmospheric fields exhibit multifractal characteristics over wide ranges of scale. These findings motivate a study of transport phenomena in multifractal media, particularly diffusion. In studying the diffusion properties of one-dimensional universal multifractal resistivity fields, a relation for the diffusion exponent $d sb{w}$ is derived and is found to depend only on $K(-1)$, the value of the moment scaling function $K(q)$ of the resistivity field for the $q=-1 sp{th}$ order statistical moment. This relation is subsequently verified through Monte Carlo simulations of diffusion on these systems. The one-to-one correspondence that exists between statistical moments and orders of singularity suggests that one order of singularity, namely $ gamma sb{-1}$, is of special importance to diffusion on multifractals, as is confirmed by simulations performed using fields that have been thresholded. Although convergence is quite slow, in the limit of an infinitely large range of scales a dynamical phase transition occurs about this particular singularity. The relation derived for the diffusion exponent breaks down for those multifractals where the $q=-1 sp{th}$ order moment diverges, which is typical of a multifractal phase transition. In these cases $d sb{w}$ must be estimated by taking into account the sample size.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.26148 |
| Date | January 1994 |
| Creators | Silas, Patricia K. (Patricia Katherine) |
| Contributors | Lovejoy, Shaun (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001403782, proquestno: MM94526, Theses scanned by UMI/ProQuest. |
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