title: Noise-driven interfaces and their macroscopic representation.
abstract: 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.
authors.affiliation: Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.
authors.forename: Marco
authors.initials: M
authors.lastname: Dentz
authors.affiliation: Institute of Fluid Mechanics in Civil Engineering, Leibniz Universität Hannover, Hanover, Germany.
authors.forename: Insa
authors.initials: I
authors.lastname: Neuweiler
authors.affiliation: Géosciences Rennes, UMR CNRS 6118, Université de Rennes 1, Rennes, France.
authors.forename: Yves
authors.initials: Y
authors.lastname: Méheust
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Tartakovsky