Ultrametric Cantor sets and Origin of Anomalous Diffusion

Details Ultrametric Cantor sets and Origin of Anomalous Diffusion Ultrametric Cantor sets and Origin of Anomalous Diffusion

2010-08-13

arxiv.org/abs/1008.2366v1

Mathematics

Classical Analysis and ODEs

Latex 2e, 12 pages

Scientific paper

The anomalous mean square fluctuations are shown to arise naturally from the ordinary diffusion equation interpreted scale invariantly in a formalism endowing real numbers with a nonarchimedean multiplicative structure. A variable $t$ approaching 0 linearly in the ordinary analysis is shown to enjoy instead a sublinear $t\log t^{-1}$ flow in the presence of this scale invariant structure. Diffusion on an ultrametric Cantor set is also generically subdiffusive with the above sublinear mean square deviation. The present study seems to offer a new interpretation of a possible emergence of complex patterns from an apparently simple system.

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