Epitaxial crystal growth is often modelled as motion of
a geometrical interface, such as a smooth surface or
a set of discrete facets or steps.
However, the equations of motion of these interfaces
depend on the physical system being modelled.
This talk will describe some illustrative examples,
each requiring different equations of motion to
describe a different regime of epitaxial growth.
In particular, a classic continuum model can be
generalized to treat growth far from thermodynamic
equilibrium. The generalized model exhibits
unexpected behavior with important practical implications.
Some problems in formulating consistent continuum models
will be discussed.
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