Noise-driven interfaces and their macroscopic representation.
Noise-driven interfaces and their macroscopic representation.
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噪声驱动的界面及其宏观表示
DOI：
10.1103/physreve.94.052802
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
D. M. Tartakovsky
中科院分区：
文献类型：
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作者：
I. Neuweiler;Y. Méheust;D. M. Tartakovsky
本文研究了一维随机界面生长模型中噪声驱动界面的宏观表示。界面的宏观特征在于饱和度，其通过具有0和1之间的值的平滑变化的相场来表示波动的尖锐界面。我们确定一点界面高度统计的爱德华-威尔金森（EW）和Kadar-Paris-Zhang（KPZ）模型，以确定明确的确定性方程的相位饱和度为他们每个人。虽然我们得到精确的结果EW模型，我们开发了高斯封闭近似的KPZ模型。我们确定了一个界面压缩项，这是与垂直于生长方向的传质，和扩散项，往往会增加界面宽度。界面压缩率取决于沿界面沿着的介观传质过程，并且在这个意义上提供了介观和宏观界面动力学之间的关系。这些结果揭示了中尺度和宏观尺度界面模型之间的关系，并提供了一个系统的框架，随机界面动力学的升级。
We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models indimensions. 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.