Universal Dynamics of Phase-Field Models for Dendritic Growth
  We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field equations are operating in their appropriate sharp interface limit. The long time steady state results are all in agreement with solvability theory. No computational advantage accrues from using a thermodynamically consistent phase-field model. 
Yung-Tae Kim (1), Nikolas Provatas (1 and 2), Nigel Goldenfeld (1),   Jonathan Dantzig (2) ((1) University of Illinois at Ur...