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Cite Details

M. Dentz, I. Neuweiler, Y. Meheust and D. M. Tartakovsky, "Noise-driven interfaces and their macroscopic representation", Phys. Rev. E, vol. 94, no. 5, doi:10.1103/PhysRevE.00.002800, pp. 052802, 2016


We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1 + 1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

BibTeX Entry

author = {M. Dentz and I. Neuweiler and Y. Meheust and D. M. Tartakovsky},
title = {Noise-driven interfaces and their macroscopic representation},
year = {2016},
urlpdf = {},
journal = {Phys. Rev. E},
volume = {94},
number = {5},
doi = {10.1103/PhysRevE.00.002800},
pages = {052802}