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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). We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one. We compare this two contributions with the ones obtained for two directed percolation deppining models (DPD): the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] and the Buldyrev et al. model [Phys. Rev. A 45, R8313 (1992)] by Braunstein al. [J. Phys. A 32, 1801 (1999); Phys. Rev. E 59, 4243 (1999)]. Even these models have being classified in the same universality class that the QKPZ the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. These results suggest that the QKPZ equation does not describe properly the DPD models even when the exponents derived from this equation are similar to the one obtained from simulations of these models.
We study the stochastically driven conserved Kardar-Parisi-Zhang (CKPZ) equation with quenched disorders. Short-ranged quenched disorders is found to be a relevant perturbation on the pure CKPZ equation at one dimension, and as a result, a new univer
We show that d+1-dimensional surface growth models can be mapped onto driven lattice gases of d-mers. The continuous surface growth corresponds to one dimensional drift of d-mers perpendicular to the (d-1)-dimensional plane spanned by the d-mers. Thi
Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a
We use the optimal fluctuation method to evaluate the short-time probability distribution $mathcal{P}left(H,L,tright)$ of height at a single point, $H=hleft(x=0,tright)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface $hleft(x,tright)$ on a ring