Comparison of descriptor analysis with effective medium approximations for evaluating the admittance of large-scale three-dimensional RLC networks

Comparison of descriptor analysis with effective medium approximations for evaluating the admittance of large-scale three-dimensional RLC networks | 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 Article Comparison of descriptor analysis with effective medium approximations for evaluating the admittance of large-scale three-dimensional RLC networks Henrique Mohallem Paiva, Roberto Kawakami Harrop Galvão, José Roberto Colombo Junior, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7792283/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract We discuss the modelling of networks composed of a mixture of capacitors, inductors and resistors, and investigate the relation between their composition and admittance response. Such networks can be employed as lumped-parameter models for composite materials containing conductive, resonant and insulating grains. The proposed models are also of further relevance to the modelling of electromechanical and electrochemical systems governed by integro-differential equations as well as other flow processes in randomly connected physical systems. The dynamics of the excited networks are studied using a model in descriptor form derived from a randomized incidence matrix. The computational modelling further benefits from sparse matrix representations which enable the frequency-domain simulation of large networks. We show that the descriptor model formulation is in good agreement with the effective medium approximation (EMA) as extended for three elements of differing conductivity and provides an alternative to existing percolation, spectral density approaches, as well as Archie’s law of dispersion and Kohlrausch-Williams-Watts (KWW) models. An emergent behaviour for different connectivity realizations is observed. Changes in the network composition can be used to tune the emergent responses. Applications in nano-science, biosciences, and complex systems research are discussed. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 11 Mar, 2026 Reviews received at journal 10 Mar, 2026 Reviewers agreed at journal 15 Feb, 2026 Reviewers agreed at journal 25 Jan, 2026 Reviewers agreed at journal 28 Oct, 2025 Reviews received at journal 17 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers invited by journal 14 Oct, 2025 Editor invited by journal 10 Oct, 2025 Editor assigned by journal 08 Oct, 2025 Submission checks completed at journal 08 Oct, 2025 First submitted to journal 06 Oct, 2025 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7792283","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":534615746,"identity":"9f08da92-8e10-4656-a969-c7b3ae1ce249","order_by":0,"name":"Henrique Mohallem Paiva","email":"","orcid":"","institution":"Institute of Technology and Leadership (Inteli)","correspondingAuthor":false,"prefix":"","firstName":"Henrique","middleName":"Mohallem","lastName":"Paiva","suffix":""},{"id":534615747,"identity":"53acf846-94ca-4ca7-bffa-bf5e27016c9d","order_by":1,"name":"Roberto Kawakami Harrop Galvão","email":"","orcid":"","institution":"Instituto 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Such networks can be employed as lumped-parameter models for composite materials containing conductive, resonant and insulating grains. The proposed models are also of further relevance to the modelling of electromechanical and electrochemical systems governed by integro-differential equations as well as other flow processes in randomly connected physical systems. The dynamics of the excited networks are studied using a model in descriptor form derived from a randomized incidence matrix. The computational modelling further benefits from sparse matrix representations which enable the frequency-domain simulation of large networks. We show that the descriptor model formulation is in good agreement with the effective medium approximation (EMA) as extended for three elements of differing conductivity and provides an alternative to existing percolation, spectral density approaches, as well as Archie’s law of dispersion and Kohlrausch-Williams-Watts (KWW) models. An emergent behaviour for different connectivity realizations is observed. Changes in the network composition can be used to tune the emergent responses. 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