A Curvature-Spectral Framework for Comparing Kelvin and Weaire-Phelan Foam Structures

A Curvature-Spectral Framework for Comparing Kelvin and Weaire-Phelan Foam Structures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Curvature-Spectral Framework for Comparing Kelvin and Weaire-Phelan Foam Structures Md. Rad Sarar Anando This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7219534/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We present a novel geometric and spectral approach to compare the energy efficiency of 3D foam structures, focusing on the classic Kelvin foam and the Weaire-Phelan (WP) structure. Using differential geometric analysis and spectral graph theory, we construct a symbolic energy model based on mean curvature and Laplacian eigenvalues. We prove two new theorems linking curvature flow energy to spectral gap rigidity, and validate our claims with analytical bounds and numerical visualization. This hybrid method provides a symbolic foundation for foam optimization, extending prior numerical-only approaches. Curvature-Spectral Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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