Interface field based methods for multiphase transformations

Title: A generalized field method for multiphase transformations using interface fields

Authors: I Steinbach and F Pezzolla

Source: Physica D: Nonlinear Phenomena, Volume 134, Issue 4, 10 December 1999, Pages 385-393

Abstract: The recently developed multiphase field method, describing the interaction between an arbitrary number of individual phase fields with individual characteristics, is reformulated by the use of interface fields. This reformulation allows for the decomposition of the nonlinear multiphase field interactions into pairwise interaction of interface fields. This removes some difficulties in the treatment of triple points or higher order interactions that occurred in the original model. The interface fields being defined in a (2^Ñ) dimensional space, where Ñ is the order of the multiple point, can be interpreted being the generalized coordinates for this variational problem. The considered example of a multiphase change problem indicates clearly that a relaxation ansatz for the evolution of the field variables towards the minimum of the free energy is warranted only for generalized coordinates, while a relaxation ansatz using functionally dependent variables and the Lagrange formalism in general mixes time and energy scales.

Note: Hat Tip: Deep.