Matching conditions in atomistic-continuum modeling of materials

A new class of matching conditions between the atomistic and continuum regions is presented for the multiscale 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.