This is the first account of the history of our understanding of, and ability to model,
solidification microstructures. Its objective is to retrace the scientific steps made, from the …

Publisher Summary This chapter focuses on the Cahn–Hilliard equation. In the context of the
Cahn–Hilliard equation, the two components could refer, for example, to a system with two …

This comprehensive and self-contained, one-stop source discusses phase-field
methodology in a fundamental way, explaining advanced numerical techniques for solving …

In an effort to unify the various phase-field models that have been used to study
solidification, we have developed a class of phase-field models for crystallization of a pure …

We study the limiting behavior of solutions to appropriately rescaled versions of the Allen‐
Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish …

Using detailed asymptotic analyses of the dynamics of the phase-field model, we show that
the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as …

The inclusion of anisotropic surface free energy and anisotropic linear interface kinetics in
phase-field models is studied for the solidification of a pure material. The formulation is …

We study dendritic microstructure evolution using an adaptive grid, finite element method
applied to a phase-field model. The computational complexity of our algorithm, per unit time …

We study the evolution of solidification microstructures using a phase-field model computed
on an adaptive, finite element grid. We discuss the details of our algorithm and show that it …

Models for phase separation and their mathematics Page 1 Electronic Journal of Differential
Equations, Vol. 2000(2000), No. 48, pp. 1–26. ISSN: 1072-6691. URL: http://ejde.math.swt.edu …