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The similarity group and anomalous diffusion equations

Content Provider	Scilit
Author	Schulzky, C. Davison, Matt Franz, A. Hoffmann, K. H.
Copyright Year	2000
Description	Journal: Journal of Physics A: General Physics A number of distinct differential equations, known as generalized diffusion equations, have been proposed to describe the phenomenon of anomalous diffusion on fractal objects. Although all are constructed to correctly reproduce the basic subdiffusive property of this phenomenon, using similarity methods it becomes very clear that this is far from sufficient to confirm their validity. The similarity group that they all have in common is the natural basis for making comparisons between these otherwise different equations, and a practical basis for comparisons between the very different modelling assumptions that their solutions each represent. Similarity induces a natural space in which to compare these solutions both with one another and with data from numerical experiments on fractals. It also reduces the differential equations to (extra-) ordinary ones, which are presented here for the first time. It becomes clear here from this approach that the proposed equations cannot agree even qualitatively with either each other or the data, suggesting that a new approach is needed.
Related Links	http://iopscience.iop.org/article/10.1088/0305-4470/33/31/305/pdf
Ending Page	5511
Page Count	11
Starting Page	5501
ISSN	00223689
DOI	10.1088/0305-4470/33/31/305
Journal	Journal of Physics A: General Physics
Issue Number	31
Volume Number	33
Language	English
Publisher	IOP Publishing
Publisher Date	2000-07-28
Access Restriction	Open
Subject Keyword	Journal: Journal of Physics A: General Physics Fluids and Plasmas Physics Differential Equation Diffusion Equation Anomalous Diffusion Difference Equation
Content Type	Text
Resource Type	Article

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