2003/03/31 by Eytan Katzav · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.031607
published as Phys. Rev. E 68, 031607 (2003) · 11 pages
arxiv created 2003/07/08 · openalex publication_date 2003/09/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.