Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases

Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases | 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 Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases Rameez Farooq Shah, syed rashid ahmad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8575250/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 establish universal scaling laws and quantify aging in three-dimensional uniformly heatedhard sphere granular gases through large-scale event-driven molecular dynamics (N = 500,000).We report three primary quantitative discoveries: (i) The characteristic energy decay time exhibitsa universal inverse scaling τ0 ∝ ϵ−1.03±0.02 with the dissipation parameter ϵ = 1 − e2. (ii) Thesteady-state temperature follows a precise power-law Tsteady ∝ ϵ−1.51±0.03, reflecting the non-linearbalance between thermostat heating and collisional dissipation. (iii) The velocity autocorrelationfunction ¯A(τw,τ) demonstrates pronounced aging, with decay rates λ following a power-law slowingdown λ(τw) ∝ τ−0.82±0.05w. These results establish the first 3D quantitative benchmarks for aging indriven dissipative gases, where near-Gaussian statistics persist despite extreme structural clustering. PACS numbers: 45.70.-n, 05.20.Dd, 05.70.Ln, 47.70.Nd Full Text Additional Declarations No competing interests reported. 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. 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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-8575250","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":577517171,"identity":"49caa912-0486-40d2-afda-2e4ef78d21f4","order_by":0,"name":"Rameez Farooq Shah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYJACZgaGA3IgxoEHpGgxBmtJIEVLYgOIRZQW82nHH38uqLmTPj/s8EOgLXZyug0EtMjcTkiTnnHsWe7G22kGQC3JxmYHCGiRkE44xszDdjh34+wEkJYDidsIa0ls/szz73C64ez0D8RqSWaQ5m07nCAvnUO0LWls0rx9hw03SOcUHEgwIMov6Y8/83w7LC8/O33zhw8VdnIEtcCBAVilAbHKQUC+gRTVo2AUjIJRMKIAAEi0Reh7uHJwAAAAAElFTkSuQmCC","orcid":"","institution":"Jamia Millia Islamia","correspondingAuthor":true,"prefix":"","firstName":"Rameez","middleName":"Farooq","lastName":"Shah","suffix":""},{"id":577517172,"identity":"b12bbd5b-eaa5-4644-8bd4-dbea2ff347ea","order_by":1,"name":"syed rashid ahmad","email":"","orcid":"","institution":"Jamia Millia Islamia","correspondingAuthor":false,"prefix":"","firstName":"syed","middleName":"rashid","lastName":"ahmad","suffix":""}],"badges":[],"createdAt":"2026-01-11 18:23:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8575250/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8575250/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100825175,"identity":"dd68cc53-ea48-4520-91d5-f662ce279391","added_by":"auto","created_at":"2026-01-21 18:54:53","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3600,"visible":true,"origin":"","legend":"","description":"","filename":"50e25020d4da49728bc10c99e0b875dd.json","url":"https://assets-eu.researchsquare.com/files/rs-8575250/v1/fc6055dd3a9098ef0fdd42c1.json"},{"id":100825215,"identity":"9dcb1b08-faa5-41c9-b46a-32f38ddeb31c","added_by":"auto","created_at":"2026-01-21 18:54:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":352339,"visible":true,"origin":"","legend":"","description":"","filename":"UniversalAgingDynamics.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8575250/v1_covered_552ac664-8752-4b9d-8e6b-888f699deb66.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Universal Aging Dynamics and Scaling Laws in Three-Dimensional Driven Granular Gases","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8575250/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8575250/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe establish universal scaling laws and quantify aging in three-dimensional uniformly heatedhard sphere granular gases through large-scale event-driven molecular dynamics (N = 500,000).We report three primary quantitative discoveries: (i) The characteristic energy decay time exhibitsa universal inverse scaling τ0 ∝ ϵ−1.03±0.02 with the dissipation parameter ϵ = 1 − e2. 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