3:00 p.m., Friday (Feb. 1)
Math Annex 1100
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.