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

J.A. Mann and W.A. Woyczynski

Physica A: Statistical Mechanics and its Applications, 2001, vol. 291, issue 1, 159-183

Abstract: 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.

Keywords: Fractal interfaces; Anomalous diffusion; Lévy flight; Fractal Burgers-KPZ equation (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:291:y:2001:i:1:p:159-183

DOI: 10.1016/S0378-4371(00)00467-2

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