Sharp-Interface Limit of a Fluctuating Phase-Field Model

Details Sharp-Interface Limit of a Fluctuating Phase-Field Model Sharp-Interface Limit of a Fluctuating Phase-Field Model

2004-09-28

arxiv.org/abs/cond-mat/0409707v2

Physics

Condensed Matter

Materials Science

21 pages, 1 figure, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.71.061603

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system.

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