Department Colloquium
Department of Mathematics
Princeton University
March 28th, 2001
Flowing crystals: Some Mathematical Challenges Posed by Materials
Science
During the past 30 years, there has been much mathematical
activity concerning minimal surfaces,
soap films and soap bubble clusters.
There has also been much mathematical activity concerning
motion by mean curvature and other motions which reduce surface area.
Simultaneously, the interaction
of mathematics and materials science has
grown. Most metals, semiconductors,
and ceramics are made up of atoms
in locally ordered arrays, called crystals,
which make interfaces with
other materials or with crystals having different orientations. The
interfaces are often regarded as two-dimensional surfaces which
are somewhat like a soap bubble cluster.
Furthermore, crystals can grow or
shrink, with reduction of surface
energy often a major influence on that
motion. The ways in which crystals
are both like and unlike soap films leads
to some fascinating mathematical problems.
Results that have been proved, new problems that have been recently
formulated, and long-standing open problems will be surveyed.