Nucleation in the One-Dimensional Stochastic Cahn-Hilliard Model

  • Despite their misleading label, rare events in stochastic systems are central to many applied phenomena. In this paper, we concentrate on one such situation - phase separation through homogeneous nucleation in binary alloys as described by the stochastic partial differential equation model due to Cahn, Hilliard, and Cook. We show that in the limit of small noise intensity, nucleation can be explained by the stochastically driven exit from the domain of attraction of an asymptotically stable homogeneous equilibrium state for the associated deterministic model. Furthermore, we provide insight into the subsequent nucleation dynamics via the structure of the attractor of the model in the absence of noise.

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Author:Dirk BlömkerORCiDGND, Bernhard Gawron, Thomas WannerORCiDGND
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-18)
Year of first Publication:2009
Publishing Institution:Universität Augsburg
Contributing Corporation:George Mason University, RWTH Aachen
Release Date:2009/07/17
Tag:Nichtlineare partielle Differentialgleichung; Musterbildung
Cahn-Hilliard-Cook model; nucleation; stochastic partial differential equation; domain exit
GND-Keyword:Stochastische partielle Differentialgleichung; Cahn-Hilliard-Gleichung; Parabolische Differentialgleichung
Erschienen in Discrete and Continuous Dynamical Systems, 27, 1, S. 25-52,
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand