{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/microscopic-patterns-in-the-2d-phase-field","title":"Microscopic Patterns in the 2D Phase-Field-Crystal Model","arxiv_id":"2102.02338","date":"2021-02-03","proceeding":null,"authors":["Gabriel Martine-La Boissoniere","Rustum Choksi","Jean-Philippe Lessard"],"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.","url_abs":"https://arxiv.org/abs/2102.02338v1","url_pdf":"https://arxiv.org/pdf/2102.02338v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"microscopic-patterns-in-the-2d-phase-field","repo_url":"https://github.com/gmartinemath/pfc-steady-states","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}