{"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/crystal-ball-a-simple-model-for-phase","title":"Crystal Ball: A Simple Model for Phase Transitions on a Classical Spherical Lattice","arxiv_id":"2410.04311","date":"2024-10-05","proceeding":null,"authors":["Aidan Bachmann","Pierre-Alexandre Gourdain","Eric G. Blackman"],"abstract":"When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to a parametric surface, focusing specifically on the case of a sphere, as in the Thomson problem. We initialize $N$ total Boron nuclei as point particles on the surface of a sphere, allowing the particles to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove $N_{rm}$ particles, forcing the system to rearrange into a new equilibrium. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of $N$ and $N_{rm}$. For certain values of $N$, we find an order of magnitude energy gain when increasing $N_{rm}$ from 1 to 6, indicating that it may be possible to engineer a lattice that maximizes the energy output.","url_abs":"https://arxiv.org/abs/2410.04311v1","url_pdf":"https://arxiv.org/pdf/2410.04311v1.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":"crystal-ball-a-simple-model-for-phase","repo_url":"https://github.com/AidanBachmann/Crystal-Ball-Public","is_official":1,"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}