Growing fractal interfaces in the presence of self-similar hopping surface diffusion

We propose and study an analytic model for growing interfaces in the presence of Brownian diffusion and hopping transport. The model is based on a continuum formulation of mass conservation at the interface, including reactions. The Burgers-KPZ equation for the rate of elevation change emerges after...

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Bibliographic Details
Published in:Physica A 2001-03, Vol.291 (1), p.159-183
Main Authors: Mann Jr, J.A., Woyczynski, W.A.
Format: Article
Language:English
Subjects:
Anomalous diffusion
Fractal Burgers-KPZ equation
Fractal interfaces
Lévy flight
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Summary:We propose and study an analytic model for growing interfaces in the presence of Brownian diffusion and hopping transport. The model is based on a continuum formulation of mass conservation at the interface, including reactions. The Burgers-KPZ equation for the rate of elevation change emerges after a number of approximations are invoked. We add to the model the possibility that surface transport may be by a hopping mechanism of a Lévy flight, which leads to the (multi)fractal Burgers-KPZ model. The issue how to incorporate experimental data on the jump length distribution in our model is discussed and controlled algorithms for numerical solutions of such fractal Burgers-KPZ equations are provided.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(00)00467-2