Szendro IG, López JM, Rodríguez MA. Localization in disordered media, anomalous roughening, and coarsening dynamics of faceted surfaces.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007;
76:011603. [PMID:
17677460 DOI:
10.1103/physreve.76.011603]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2007] [Revised: 05/30/2007] [Indexed: 05/16/2023]
Abstract
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 eta(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.
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