Eur. Phys. J. B 21, 289-294 (2001)
https://doi.org/10.1007/s100510170204

Growing mechanisms in the QKPZ equation and the DPD models

¹ Dipartamento di Scienze Fisiche, Universitá di Napoli "Federico II" , Complesso Universitario di Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy and INFM, Unitá di Napoli, Napoli, Italy
² Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Argentina

Corresponding author: ^a tasio@na.infn.it, anastasio.diaz@na.infn.it

Received: 7 April 2000
Revised: 7 March 2001
Published online: 15 May 2001

Abstract

The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)] with quenched noise (QKPZ) [Phys. Rev. Lett. 74, 920 (1995)]. We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one in order to compare them with the local and the lateral contributions obtained for the directed percolation depinning models (DPD) introduced independently by Tang and Leschhorn [Phys. Rev A 45, R8309 (1992)] and Buldyrev et al. [Phys. Rev A 45, R8313 (1992)]. These models are classified in the same universality class of the QKPZ although the mechanisms of growth are quite different. In the DPD models the lateral contribution is a coupled effect of the competition between the local growth and the lateral one. In these models the lateral contribution leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness.