Fluctuations in the phase-field model of solidification

We develop two analytical solutions for thermodynamic fluctuations that are present in the phase-field model of solidification. One solution deals wit h fluctuations in an isothermal single phase system. The other deals with f luctuations in a two-phase isothermal system having a planar diffuse interf ace. Explicit formulae are obtained in one, two and three dimensions. In th e case of two-phase system, fluctuations of the phase field are somewhat su ppressed in the interface region. These solutions provide targets for testi ng numerical solutions. (C) 2000 Published by Elsevier Science B.V. All rig hts reserved.