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Localization in disordered media, anomalous roughening, and coarsening dynamics

Journal: Physical Review E
Year: 2007   Volume: 76
Initial page: 11603  
Status: Published
In this status since: 20 Jul 2007
PDF file: 2007_Szendro_pre_a.pdf
DOI: 10.1103/PhysRevE.76.011603
Szendro, I., López, J.M.,

We study a surface growth model related to the Kardar-Parisi-Zhang equation for nonequilibrium kinetic
roughening, but where the thermal noise is replaced by a static columnar disorder x. This model is one of
the many representations of the problem of particle diffusion in trapping or amplifying disordered media. We find that probability localization in the latter translates into facet formation in the equivalent surface growth problem. Coarsening of the pattern can therefore be identified with the diffusion of the localization center. The emergent faceted structure gives rise to nontrivial scaling properties, including anomalous surface roughening in excellent agreement with an existing conjecture for kinetic roughening of faceted surfaces. In a wider context, our study sheds light onto the scaling properties in other systems displaying this kind of patterned surface.