KPZ equation with realistic short-range-correlated noise

Abstract

We study a realistic simulation model for the propagation of slow-combustion fronts in paper. In the simulations the deterministic part of the dynamics is that of the KPZ equation. The stochastic part, including in particular the short-range noise correlations, is taken from images of the structure of real paper samples. The parameters of the simulations are determined by using an inverse method applied to the experimental front data and by comparing the simulated and the experimental effective-noise distributions. Our model predicts well the shape of the spatial and temporal correlation functions, including the location of the crossovers from short-range (SR) to long-range (LR) behavior. The values of the exponents \(\chi_{\rm SR}\), \(\beta_{\rm SR}\), \(\chi_{\rm LR}\) and \(\beta_{\rm LR}\) agree with the experimental ones. The apparent SR exponents are found to be the same for different types of quenched noise. The correlated noise is shown to have a major contribution to the effective, ‘measured’ nonlinearity. We discuss in detail how to implement the noise so as to obtain a realistic simulation model.