A variational formulation for modeling a protium hydrogen molecular ionization and notes on the Energy equation, the first Maxwell one and the Entropy formula

A variational formulation for modeling a protium hydrogen molecular ionization and notes on the Energy equation, the first Maxwell one and the Entropy formula | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 4 August 2025 V1 Latest version Share on A variational formulation for modeling a protium hydrogen molecular ionization and notes on the Energy equation, the first Maxwell one and the Entropy formula Authors : Fabio Botelho 0000-0002-3890-8263 [email protected] and Fabio Silva Botelho Authors Info & Affiliations https://doi.org/10.22541/au.175433589.93254123/v1 244 views 140 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This article develops a variational formulation for modeling a protium hydrogen molecular ionization obtained through a high temperature scalar field and an appropriate electric one action. The results are based on standard tools of calculus of variations and optimization theory. Finally, we highlight the context here addressed is essentially an Euler-Bernoullian one and includes the establishment of a new approximate Bernoulli-interacting-gas type equation. Supplementary Material File (hydrogen-july-2025-18.pdf) Download 334.60 KB Information & Authors Information Version history V1 Version 1 04 August 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords 76n15 hydrogen molecular system ionization lagrange multipliers optimization. msc: 76a02 strong variational formulations Authors Affiliations Fabio Botelho 0000-0002-3890-8263 [email protected] View all articles by this author Fabio Silva Botelho Department of Mathematics, Federal University of Santa Catarina, UFSC Florianópolis View all articles by this author Metrics & Citations Metrics Article Usage 244 views 140 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Fabio Botelho, Fabio Silva Botelho. A variational formulation for modeling a protium hydrogen molecular ionization and notes on the Energy equation, the first Maxwell one and the Entropy formula. Authorea . 04 August 2025. DOI: https://doi.org/10.22541/au.175433589.93254123/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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