Dynamics of Layered Interfaces Arising from Phase Boundaries

Simulation for microstructure evolution of Al-Si alloys in solidification process

“…Then, Caginalp [5][6][7], Fife and Gill [8,9] suggested that when the interface width is near zero, PFM would be the sharp interface model, and they firstly introduced the anisotropic factor. Fix [10] carried out the numerical solution of phase field equations for the first time.…”

Phase-field models for the approximation of the willmore functional and flow

“…In particular, we shall derive explicitly each approximating gradient flow and, using the matched asymptotic expansion method [6,8,18, 23], we will show that, at least formally and for smooth interfaces, there is convergence to the Willmore flow, at least in dimensions 2 and 3 for all flows, and in any dimension for some of them. The general question "if a sequence of functionals Γ-converges to a limit functional, is there also convergence of the associated flows?"…”

Phase transitions in materials with thermal memory: The case of unequal conductivities

“…Let us first consider a simplified model ( [ 6] for example) where the transition zone is moving at constant dimensionless velocity.…”