Diffuse Interfaces: Modeling, Analysis and Computation

Physical interfaces have most commonly been regarded as mathematical surfaces, across which there may be a discontinuity of physical quantities or their derivatives. An alternative way to model them is by a continuous transition layer of small but finite thickness. Recent interest in both realistic modeling and computer simulation have stimulated considerable interest in this viewpoint.

In this talk, an overview of the theory of diffuse interfaces is presented. Historical developments from its roots in 19th century physics to the present will be outlined, pointing out the diversity of possible applications as well as outstanding challenges in the field. The connection of diffuse interface models to free boundary problems and geometrical motions will also be explained. Finally, computational methods for interface problems will be reviewed and compared to those based on diffuse interface theory.