Scaling Relations and Exponents in the Growth of Rough Interfaces Through Random Media

TL;DR

This paper models the growth of rough interfaces in random media using a stochastic equation with quenched noise, deriving exponents that match experimental and simulation results through scaling arguments.

Contribution

It introduces a method to compute interface roughness exponents from a stochastic model with quenched noise using the Novikov theorem and scaling analysis.

Findings

Derived roughness exponents consistent with experiments

Established effective temporal correlations in interface growth

Validated the model with numerical simulations

Abstract

The growth of a rough interface through a random media is modelled by a continuous stochastic equation with a quenched noise. By use of the Novikov theorem we can transform the dependence of the noise on the interface height into an effective temporal correlation for different regimes of the evolution of the interface. The exponents characterizing the roughness of the interface can thus be computed by simple scaling arguments showing a good agreement with recent experiments and numerical simulations.