Spectral Theory Correction of Nonlinear Calibration: A Perturbative Framework

Spectral Theory Correction of Nonlinear Calibration: A Perturbative Framework | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 17 December 2025 V1 Latest version Share on Spectral Theory Correction of Nonlinear Calibration: A Perturbative Framework Author : Cesar A. de Mello 0000-0002-6730-9593 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176596214.49534960/v1 217 views 70 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The Debye–Hückel (DH) theory remains a foundational framework for quantifying electrostatic interactions in electrolyte solutions, yet its classical formulation obscures the geometric and spectral structures that govern ionic activity at the microscopic level. Here a topological and operator-theoretic reinterpretation of DH is developed by embedding the Poisson–Boltzmann operator into a compact, self-adjoint spectral problem on weighted Sobolev spaces. Ionic activities are shown to arise from deformations of a principal eigenvalue branch whose curvature is controlled by local topological indices associated with field-line bundles. The DH limiting law is recovered as the first-order perturbation of this eigenbranch, while extended activity-coefficient models are encoded as higher-order spectral corrections. A closed-form representation of the DH potential is obtained via a functional calculus based on the resolvent of the Laplace–Yukawa operator, establishing a precise analogy with spectral calibration techniques in analytical chemistry. This perspective clarifies the geometric meaning of screening, unifies empirical extensions of DH, and provides a rigorous, coordinate-free route to generalizations relevant for concentrated electrolytes, multivalent systems and complex media. Supplementary Material File (spectral_theory_correction_of_nonlinear_calibration.pdf) Download 1.24 MB Information & Authors Information Version history V1 Version 1 17 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords activity coefficients debye–hückel theory eigenvalue curvature functional calibration nonlinear calibration self-adjoint operators spectral perturbation theory spectral theory yukawa operator Authors Affiliations Cesar A. de Mello 0000-0002-6730-9593 [email protected] Cosmo Physics Labs View all articles by this author Metrics & Citations Metrics Article Usage 217 views 70 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Cesar A. de Mello. Spectral Theory Correction of Nonlinear Calibration: A Perturbative Framework. Authorea . 17 December 2025. DOI: https://doi.org/10.22541/au.176596214.49534960/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 . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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