Microscopic patterns in the 2D phase-field-crystal model

Abstract Using the recently developed theory of rigorously validated numerics, we address phase-field-crystal model at microscopic (atomistic) level. We show existence critical points and local minimizers associated with ‘classical’ candidates, grain boundaries, localized patterns. further dynamical relationships between observed patterns for fixed parameters across parameter space, then formulate several conjectures on connections (or orbits) steady states.