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

TL;DR

This paper rigorously analyzes the 2D Phase-Field-Crystal model at the microscopic level, establishing existence of critical points, local minimizers, and exploring dynamical relationships between patterns and steady states.

Contribution

It introduces a validated numerical approach to prove the existence of critical points and local minimizers in the PFC model, and investigates their dynamical connections.

Findings

Existence of critical points and local minimizers for the PFC model.

Identification of patterns such as grain boundaries and localized structures.

Formulation of conjectures on dynamical connections between steady states.

Abstract

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