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Abstract: The anomalous mean square fluctuations are shown to arise naturally from theordinary diffusion equation interpreted scale invariantly in a formalismendowing real numbers with a nonarchimedean multiplicative structure. Avariable $t$ approaching 0 linearly in the ordinary analysis is shown to enjoyinstead a sublinear $t\log t^{-1}$ flow in the presence of this scale invariantstructure. Diffusion on an ultrametric Cantor set is also genericallysubdiffusive with the above sublinear mean square deviation. The present studyseems to offer a new interpretation of a possible emergence of complex patternsfrom an apparently simple system.



Author: Dhurjati Prasad Datta, Santanu Raut, Anuja Roy Chaudhuri

Source: https://arxiv.org/



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