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Using the recently developed theory of rigorously validated numerics, weaddress the Phase-Field-Crystal (PFC) model at the microscopic (atomistic)level. We show the existence of critical points and local minimizers associatedwith "classical" candidates, grain boundaries, and localized patterns. Wefurther address the dynamical relationships between the observed patterns forfixed parameters and across parameter space, then formulate several conjectureson the dynamical connections (or orbits) between steady states.

Microscopic Patterns in the 2D Phase-Field-Crystal Model