{"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/phase-field-approach-to-optimal-packing","title":"Phase field approach to optimal packing problems and related Cheeger clusters","arxiv_id":"1706.05506","date":"2017-06-17","proceeding":null,"authors":["Beniamin Bogosel","Dorin Bucur","Ilaria Fragala"],"abstract":"In a fixed domain of $\\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\\alpha$ converges to the \"critical\" value $\\Big (\\frac{N-1}{N}\\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions.","url_abs":"http://arxiv.org/abs/1706.05506v1","url_pdf":"http://arxiv.org/pdf/1706.05506v1.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":"phase-field-approach-to-optimal-packing","repo_url":"https://github.com/bbogo/Cheeger_patch","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}