Nucleation in the one-dimensional stochastic Cahn-Hilliard model

46. Dirk Blömker, Bernhard Gawron, Thomas Wanner:
    Nucleation in the one-dimensional stochastic Cahn-Hilliard model
    Discrete and Continuous Dynamical Systems, Series A 27(1), pp. 25-52, 2010.

Abstract

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.

Links

The published version of the paper can be found at https://doi.org/10.3934/dcds.2010.27.25.

Bibtex

@article{bloemker:etal:10a,
   author = {Dirk Bl\"omker and Bernhard Gawron and Thomas Wanner},
   title = {Nucleation in the one-dimensional stochastic {C}ahn-{H}illiard model},
   journal = {Discrete and Continuous Dynamical Systems, Series A},
   year = 2010,
   volume = 27,
   number = 1,
   pages = {25--52},
   doi = {10.3934/dcds.2010.27.25}
   }