Directed percolation depinning models: Evolution equations

TL;DR

This paper derives microscopic evolution equations for interface growth with quenched noise, comparing contributions in different models and analyzing how these influence roughness near criticality.

Contribution

It introduces a simple microscopic equation for interface growth with quenched noise, linking contact and local contributions, and compares these across models.

Findings

Contact and local contributions are qualitatively similar across models.

Diffusion and contact contributions increase roughness near criticality.

The microscopic equations clarify the mechanisms behind interface roughening.

Abstract

We present the microscopic equation for the growing interface with quenched noise for the model first presented by Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. The microscopic equation allows us to express these equations in two contributions: the contact and the local one. We compare this two contributions with the ones obtained for the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] by Braunstein et al. [Physica A 266, 308 (1999)]. Even when the microscopic mechanisms are quiet different in both model, the two contribution are qualitatively similar. An interesting result is that the diffusion contribution, in the Tang and Leschhorn model, and the contact one, in the Buldyrev model, leads to an increase of the roughness near the criticality.