  We present a coupled atomistic-continuum method for the modeling of defects
and interface dynamics of crystalline materials. The method uses atomistic
models such as molecular dynamics near defects and interfaces, and continuum
models away from defects and interfaces. We propose a new class of matching
conditions between the atomistic and continuum regions. These conditions ensure
the accurate passage of large scale information between the atomistic and
continuum regions and at the same time minimize the reflection of phonons at
the atomistic-continuum interface. They can be made adaptive if we choose
appropriate weight functions. We present applications to dislocation dynamics,
friction between two-dimensional crystal surfaces and fracture dynamics. We
compare results of the coupled method and the detailed atomistic model.
