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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.
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Marco Dentz, Insa Neuweiler, Yves Méheust, Daniel Tartakovsky. Noise-driven interfaces and their macroscopic representation. Physical Review E , American Physical Society (APS), 2016, 94 (5), pp.052802. ⟨10.1103/PhysRevE.94.052802⟩. ⟨insu-01406307⟩

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