Roughening of the anharmonic Larkin model.
Phys Rev E
; 99(3-1): 032105, 2019 Mar.
Article
em En
| MEDLINE
| ID: mdl-30999460
We study the roughening of d-dimensional directed elastic interfaces subject to quenched random forces. As in the Larkin model, random forces are considered constant in the displacement direction and uncorrelated in the perpendicular direction. The elastic energy density contains an harmonic part, proportional to (∂_{x}u)^{2}, and an anharmonic part, proportional to (∂_{x}u)^{2n}, where u is the displacement field and n>1 an integer. By heuristic scaling arguments, we obtain the global roughness exponent ζ, the dynamic exponent z, and the harmonic to anharmonic crossover length scale, for arbitrary d and n, yielding an upper critical dimension d_{c}(n)=4n. We find a precise agreement with numerical calculations in d=1. For the d=1 case we observe, however, an anomalous "faceted" scaling, with the spectral roughness exponent ζ_{s} satisfying ζ_{s}>ζ>1 for any finite n>1, hence invalidating the usual single-exponent scaling for two-point correlation functions, and the small gradient approximation of the elastic energy density in the thermodynamic limit. We show that such d=1 case is directly related to a family of Brownian functionals parameterized by n, ranging from the random-acceleration model for n=1 to the Lévy arcsine-law problem for n=∞. Our results may be experimentally relevant for describing the roughening of nonlinear elastic interfaces in a Matheron-de Marsilly type of random flow.
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1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2019
Tipo de documento:
Article
País de afiliação:
Argentina
País de publicação:
Estados Unidos