Stretched exponential relaxation for growing interfaces in quenched disordered media
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AuthorDíaz Sánchez, Anastasio; Pérez Garrido, Antonio; Urbina Yeregui, Antonio; Catalá Galindo, José Damián
Knowledge AreaFísica Aplicada
SponsorsThis work was supported in part by the project No. PI-60/00858/FS/01 from the Fundación Séneca, Región de Murcia.
PublisherAmerican Physical Society
Bibliographic CitationDÍAZ SÁNCHEZ, A., PÉREZ GARRIDO, A., URBINA, A., CATALÁ, J.D. Stretched exponential relaxation for growing interfaces in quenched disordered media . Physical Review B, 66: 031403-1 - 031403-4, Septiembre, 2002. ISSN 1550-235X
KeywordsFunción de autocorrelación de dos tiempos
Transformación de Fourier
We study the relaxation for growing interfaces in quenched disordered media. We use a directed percolation depinning model introduced by Tang and Leschhorn for 1+1-dimensions. We define the two-time autocorrelation function of the interface height C(t′, t) and its Fourier transform. These functions depend on the difference of times t−t′ for long enough times, this is the steady-state regime. We find a two-step relaxation decay in this regime. The long time tail can be fitted by a stretched exponential relaxation function. The relaxation time is proportional to the characteristic distance of the clusters of pinning cells in the direction parallel to the interface and it diverges as a power law. The two-step relaxation is lost at a given wave length of the Fourier transform, which is proportional to the characteristic distance of the clusters of pinning cells in the direction perpendicular to the interface. The stretched exponential relaxation is caused by the existence of clusters ...
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