Forces due to fluctuations in the anisotropic phase-field model of solidification

Stochastic forces due to thermodynamic fluctuations are derived for the ani sotropic phase-field model of solidification, The stochastic forces turn ou t to be anisotropic. The derivation utilizes the general principles of irre versible thermodynamics. One of the forces is the divergence of the stochas tic heat flux derived by Landau and Lifshitz (Statistical Physics, Pergamon Press, Oxford, 1958). The other force is the phase-field counterpart of th e interface force introduced by Karma (Phys. Rev. E 48 (1993) 3441). (C) 19 99 Elsevier Science B.V. All rights reserved.