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Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media

L. A. Braunstein·R. C. Buceta·C. D. Archubi·G. Costanza
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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 $(\nabla h)^2$ 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.

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L. A. Braunstein, R. C. Buceta, C. D. Archubi, G. Costanza. 1999-08-24. Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media. https://doi.org/10.1103/physreve.62.3920

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