Stretched exponential relaxation for growing interfaces in quenched disordered media
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URI: http://arxiv.org/abs/cond-mat/0206545URI: http://hdl.handle.net/10317/581
ISSN: 1550-235X
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Díaz Sánchez, Anastasio; Pérez Garrido, Antonio; Urbina Yeregui, Antonio; Catalá Galindo, José DamiánÁrea de conocimiento
Física AplicadaPatrocinadores
This work was supported in part by the project No. PI-60/00858/FS/01 from the Fundación Séneca, Región de Murcia.Fecha de publicación
2002-09Editorial
American Physical SocietyCita bibliográfica
DÍAZ 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 1550-235XPalabras clave
Función de autocorrelación de dos tiemposTransformación de Fourier
Resumen
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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