We consider a system consisting of two types of particles called "water" and "ice" on d-dimensional periodic lattices. The water particles perform excluded interacting random walks (stochastic lattice gases), while the ice particles are immobile. When a water particle touches an ice particle, it immediately dies. On the other hand, the ice particle disappears after receiving the ℓth visit from water particles. This interaction models the melting of a solid with latent heat. We derive the nonlinear one-phase Stefan free boundary problem in a hydrodynamic scaling limit. Derivation of two-phase Stefan problem is also discussed.
|Number of pages||31|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|Publication status||Published - 1999 Sep|
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty