▪ Abstract The phase-field method has recently emerged as a powerful computational
approach to modeling and predicting mesoscale morphological and microstructure evolution …

This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

A phase field model for the mixture of two incompressible fluids is presented in this paper.
The model is based on an energetic variational formulation. It consists of a Navier–Stokes …

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 …

In this paper, we compute the equilibrium configurations of a vesicle membrane under
elastic bending energy, with prescribed volume and surface area. A variational phase field …

The connection between the weak theories for a class of geometric equations and the
asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established …

Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in
phase separation with the thermodynamically relevant logarithmic potentials; in particular …

In this paper, we study the three-dimensional deformation of a vesicle membrane under the
elastic bending energy, with prescribed bulk volume and surface area. Both static and …

Using balance laws for accretive force and energy in conjunction with constitutive equations
restricted so as to be compatible with the second law, we develop a theory for the study of …

A multi phase field model is presented for the investigation of the effect of transformation
strain on the transformation kinetics, morphology and thermodynamic stability in multi phase …