Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media
Statistical Mechanics
2009-10-31 v1 Disordered Systems and Neural Networks
Abstract
We present an analytical continuous equation for the Tang and Leschhorn model [Phys. Rev A {\bf 45}, R8309 (1992)] derived from his microscopic rules using a regularization procedure. As well in this approach the nonlinear term arises naturally from the microscopic dynamics even if the continuous equation is not the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. {\bf 56}, 889 (1986)] with quenched noise (QKPZ). Our equation looks like a QKPZ but with multiplicative quenched and thermal noise. The numerical integration of our equation reproduce the scaling exponents of the roughness of this directed percolation depinning model.
Cite
@article{arxiv.cond-mat/9908343,
title = {Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media},
author = {L. A. Braunstein and R. C. Buceta and C. D. Archubi and G. Costanza},
journal= {arXiv preprint arXiv:cond-mat/9908343},
year = {2009}
}
Comments
8 pages, 4 figures. Submitted to Phys. Rev. E (Rapid Comunication)