A microscopic model for Stefan’s melting and freezing problem. (English) Zbl 1097.60082

Landim, Claudio; Valle, Glauco

Ann. Probab. 34, No. 2, 779-803 (2006).

Summary: We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan’s melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy-Stefan problem.

MSC:

60K35

Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

exclusion processes; Cauchy-Stefan problem; hydrodynamic limit

References:

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