Details
Originalsprache | Englisch |
---|---|
Aufsatznummer | 052802 |
Fachzeitschrift | Physical Review E |
Jahrgang | 94 |
Ausgabenummer | 5 |
Publikationsstatus | Veröffentlicht - 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 Sachgebiete
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Mathematik (insg.)
- Statistik und Wahrscheinlichkeit
- Physik und Astronomie (insg.)
- Physik der kondensierten Materie
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Physical Review E, Jahrgang 94, Nr. 5, 052802, 07.11.2016.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -