Growing interfaces in quenched disordered media

Details Growing interfaces in quenched disordered media Growing interfaces in quenched disordered media

1999-03-05

arxiv.org/abs/cond-mat/9903096v1

Physica A, Volume 266, Issue:1-4, (1999), p 308-312

Physics

Condensed Matter

Statistical Mechanics

6 pages and 3 figures. Conference on Percolation and disordered systems: theory and applications, Giessen, Germany, (July, 199

Scientific paper

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [{\em Phys. Rev.} {\bf A 45}, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple way. Also, an equation for the interface activity density (i.e. interface density of free sites) as function of time is obtained. The microscopic equation allows us to express these equations in two contributions: the diffusion and the substratum one. All the equation shows the strong interplay between both contributions in the dynamics. A macroscopic evolution equation for the roughness is presented for this model for the critical pressure $p=0.461$. The dynamical exponent $\beta=0.629$ is analitically obtained in a simple way. Theoretical results are in excellent agreement with the Monte Carlo simulation.

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