Details
| Original language | English |
|---|---|
| Article number | 052802 |
| Journal | Physical Review E |
| Volume | 94 |
| Issue number | 5 |
| Publication status | Published - 7 Nov 2016 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Physical Review E, Vol. 94, No. 5, 052802, 07.11.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Noise-driven interfaces and their macroscopic representation
AU - Dentz, Marco
AU - Neuweiler, Insa
AU - Méheust, Yves
AU - Tartakovsky, Daniel M.
PY - 2016/11/7
Y1 - 2016/11/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84994632825&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.94.052802
DO - 10.1103/PhysRevE.94.052802
M3 - Article
AN - SCOPUS:84994632825
VL - 94
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 5
M1 - 052802
ER -