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Dynamics of Surface Roughening with Quenched Disorder

S. Havlin·L. A. N. Amaral·S. V. Buldyrev·S. T. Harrington·H. E. Stanley
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Abstract

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for percolation, from $d = 1$ to $d = 6$.

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S. Havlin, L. A. N. Amaral, S. V. Buldyrev, S. T. Harrington, H. E. Stanley. 1994-11-09. Dynamics of Surface Roughening with Quenched Disorder. https://doi.org/10.1103/physrevlett.74.4205

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