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

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

1999-08-24

arxiv.org/abs/cond-mat/9908343v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures. Submitted to Phys. Rev. E (Rapid Comunication)

Scientific paper

10.1103/PhysRevE.62.3920

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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