Microscopic patterns in the 2D phase-field-crystal model. (3rd March 2022)

• Record Type: Journal Article
• Authors: Martine-La Boissonière, Gabriel; Choksi, Rustum; Lessard, Jean-Philippe
• Is Part Of: Nonlinearity. Volume 35:Number 3(2022)
• Page Start: 1500
• Page End: 1520
• Publication Date: 2022-03-03
• Subjects: phase field crystal -- rigorously supported numerics -- radial polynomial -- grain boundary -- polycrystalline materials; 65P40; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac4d91
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Using the recently developed theory of rigorously validated numerics, we address the phase-field-crystal 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.