  A new class of matching condition between the atomistic and continuum regions
is presented for the multi-scale modeling of crystals. They 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 interface. These
matching conditions can be made adaptive if we choose appropriate weight
functions. Applications to dislocation dynamics and friction between
two-dimensional atomically flat crystal surfaces are described.
