{"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/a-large-scale-statistical-study-of-the","title":"A large-scale statistical study of the coarsening rate in models of Ostwald-Ripening","arxiv_id":"1911.03386","date":"2019-11-08","proceeding":null,"authors":["Lennon Ó Náraigh","Andrew Gloster"],"abstract":"In this article we look at the coarsening rate in two standard models of Ostwald Ripening. Specifically, we look at a discrete droplet population model, which in the limit of an infinite droplet population reduces to the classical Lifshitz--Slyozov--Wagner model. We also look at the Cahn--Hilliard equation with constant mobility. We define the coarsening rate as $\\beta=-(t/F)(d F/d t)$, where $F$ is the total free energy of the system and $t$ is time. There is a conjecture that the long-time average value of $\\beta$ should not exceed $1/3$ -- this result is summarized here as $\\langle \\beta\\rangle\\leq 1/3$. We explore this conjecture for the two considered models. Using large-scale computational resources (specifically, GPU computing employing thousands of threads), we are able to construct ensembles of simulations and thereby build up a statistical picture of $\\beta$. Our results show that the droplet population model and the Cahn--Hilliard equation (asymmetric mixtures) are demonstrably in agreement with $\\langle\\beta\\rangle\\leq 1/3$. The results for the Cahn--Hilliard equation in the case of symmetric mixtures show $\\langle\\beta\\rangle$ sometimes exceeds $1/3$ in our simulations. However, the possibility is left open for the very long-time average values of $\\langle \\beta\\rangle$ to be bounded above by $1/3$. The theoretical methodology laid out in this paper sets a path for future more intensive computational studies whereby this conjecture can be explored in more depth. \\end{abstract}","url_abs":"https://arxiv.org/abs/1911.03386v1","url_pdf":"https://arxiv.org/pdf/1911.03386v1.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":"a-large-scale-statistical-study-of-the","repo_url":"https://github.com/munstermonster/cuSten","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}